If the Temperature of a Substance Increases, What Can You Conclude About the Value of Q?

Rut Chapters

The rut chapters measures the amount of rut necessary to raise the temperature of an object or organisation by 1 degree Celsius.

Learning Objectives

Explain the enthalpy in a system with abiding volume and pressure level

Key Takeaways

Central Points

• Heat chapters is the measurable physical quantity that characterizes the amount of heat required to alter a substance'south temperature past a given amount. Information technology is measured in joules per Kelvin and given by.
• The heat capacity is an extensive holding, scaling with the size of the system.
• The heat capacity of most systems is not constant (though it can often exist treated as such). It depends on the temperature, pressure, and book of the system under consideration.

Fundamental Terms

• oestrus capacity: The amount of oestrus free energy needed to raise the temperature of an object or unit of matter by one degree Celsius; in units of joules per kelvin (J/Grand).
• enthalpy: the full amount of energy in a system, including both the internal energy and the energy needed to displace its environment

Oestrus Chapters

Heat capacity (usually denoted past a capital C, often with subscripts), or thermal chapters, is the measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount. In SI units, heat capacity is expressed in units of joules per kelvin (J/Chiliad).

An object'south heat capacity (symbol C) is defined every bit the ratio of the amount of heat energy transferred to an object to the resulting increase in temperature of the object.

[latex]\displaystyle{\text{C}=\frac{\text{Q}}{ \Delta \text{T}}.} [/latex]

Oestrus chapters is an extensive property, and then it scales with the size of the arrangement. A sample containing twice the amount of substance as some other sample requires the transfer of twice as much rut (Q) to achieve the aforementioned change in temperature (ΔT). For example, if it takes ane,000 J to oestrus a block of iron, information technology would accept 2,000 J to heat a second cake of iron with twice the mass as the offset.

The Measurement of Heat Capacity

The heat capacity of most systems is not a constant. Rather, it depends on the land variables of the thermodynamic system under report. In particular, information technology is dependent on temperature itself, as well equally on the pressure and the volume of the system, and the means in which pressures and volumes have been allowed to change while the system has passed from 1 temperature to another. The reason for this is that pressure-volume work done to the system raises its temperature past a machinery other than heating, while pressure-book work washed by the organization absorbs heat without raising the organization's temperature. (The temperature dependence is why the definition a calorie is formally the free energy needed to heat 1 g of water from 14.5 to 15.5 °C instead of generally by ane °C. )

Different measurements of heat capacity can therefore be performed, virtually commonly at constant force per unit area and abiding volume. The values thus measured are commonly subscripted (by p and 5, respectively) to signal the definition. Gases and liquids are typically also measured at constant volume. Measurements nether constant pressure produce larger values than those at abiding book because the abiding pressure values also include estrus free energy that is used to practice work to expand the substance against the abiding pressure every bit its temperature increases. This departure is specially notable in gases where values under abiding pressure are typically thirty% to 66.7% greater than those at constant volume.

Thermodynamic Relations and Definition of Oestrus Chapters

The internal free energy of a airtight arrangement changes either by adding heat to the system or by the system performing piece of work. Recalling the first constabulary of thermodynamics,

[latex]\text{dU}=\delta \text{Q}-\delta \text{W}[/latex].

For work equally a result of an increase of the organisation volume we may write,

[latex]\text{dU}=\delta \text{Q}-\text{PdV}[/latex].

If the heat is added at constant volume, then the second term of this relation vanishes and one readily obtains

[latex]\displaystyle{\left( \frac{\partial \text{U}}{\partial \text{T}}\correct) _{\text{V}}=\left( \frac{\partial \text{Q}}{\partial \text{T}}\right) _{\text{V}}=\text{C}_{\text{V}}}[/latex].

This defines the heat chapters at constant volume, C _V. Another useful quantity is the oestrus capacity at constant pressure, C _P. With the enthalpy of the system given by

[latex]\text{H}=\text{U}+\text{PV}[/latex],

our equation for dU changes to

[latex]\text{dH}=\delta \text{Q}+\text{VdP}[/latex],

and therefore, at constant force per unit area, nosotros take

[latex](\frac{\fractional \text{H}}{\partial \text{T}})_{\text{P}}=(\frac{\fractional \text{Q}}{\partial \text{T}})_{\text{P}}=\text{C}_{\text{P}}[/latex].

Specific Heat

The specific heat is an intensive holding that describes how much heat must be added to a particular substance to raise its temperature.

Learning Objectives

Summarize the quantitative relationship between rut transfer and temperature change

Key Takeaways

Key Points

• Unlike the total rut capacity, the specific rut capacity is independent of mass or volume. It describes how much heat must be added to a unit of mass of a given substance to raise its temperature past ane degree Celsius. The units of specific heat capacity are J/(kg °C) or equivalently J/(kg Thou).
• The heat capacity and the specific estrus are related by C=cm or c=C/m.
• The mass one thousand, specific heat c, change in temperature ΔT, and heat added (or subtracted) Q are related by the equation: Q=mcΔT.
• Values of specific oestrus are dependent on the properties and phase of a given substance. Since they cannot be calculated easily, they are empirically measured and available for reference in tables.

Fundamental Terms

• specific heat capacity: The amount of heat that must be added (or removed) from a unit mass of a substance to change its temperature by 1 caste Celsius. Information technology is an intensive holding.

Specific Heat

The heat capacity is an all-encompassing property that describes how much oestrus energy it takes to raise the temperature of a given organisation. Notwithstanding, information technology would be pretty inconvenient to mensurate the heat capacity of every unit of measurement of matter. What we want is an intensive property that depends but on the type and phase of a substance and tin be applied to systems of arbitrary size. This quantity is known as the specific heat capacity (or simply, the specific heat), which is the estrus capacity per unit mass of a material. Experiments bear witness that the transferred heat depends on three factors: (1) The change in temperature, (2) the mass of the system, and (3) the substance and phase of the substance. The last ii factors are encapsulated in the value of the specific heat.

Heat Transfer and Specific Rut Capacity: The rut Q transferred to cause a temperature change depends on the magnitude of the temperature alter, the mass of the organization, and the substance and phase involved. (a) The amount of estrus transferred is directly proportional to the temperature change. To double the temperature change of a mass m, you need to add together twice the heat. (b) The amount of heat transferred is also straight proportional to the mass. To cause an equivalent temperature change in a doubled mass, yous demand to add twice the rut. (c) The amount of heat transferred depends on the substance and its phase. If it takes an amount Q of heat to cause a temperature change ΔT in a given mass of copper, it will have ten.viii times that amount of heat to cause the equivalent temperature change in the same mass of water assuming no phase change in either substance.

Specific Heat Chapters: This lesson relates heat to a change in temperature. We talk over how the amount of oestrus needed for a temperature change is dependent on mass and the substance involved, and that human relationship is represented by the specific estrus capactiy of the substance, C.

The dependence on temperature change and mass are easily understood. Because the (average) kinetic energy of an atom or molecule is proportional to the absolute temperature, the internal free energy of a organization is proportional to the absolute temperature and the number of atoms or molecules. Since the transferred heat is equal to the change in the internal energy, the heat is proportional to the mass of the substance and the temperature change. The transferred heat too depends on the substance then that, for example, the heat necessary to raise the temperature is less for alcohol than for water. For the same substance, the transferred estrus also depends on the stage (gas, liquid, or solid).

The quantitative relationship between heat transfer and temperature alter contains all three factors:

[latex]\text{Q}=\text{mc}\Delta \text{T}[/latex],

where Q is the symbol for heat transfer, chiliad is the mass of the substance, and ΔT is the change in temperature. The symbol c stands for specific oestrus and depends on the textile and phase.

The specific heat is the amount of estrus necessary to change the temperature of 1.00 kg of mass by 1.00ºC. The specific rut c is a holding of the substance; its SI unit is J/(kg⋅Grand) or J/(kg⋅C). Recollect that the temperature change (ΔT) is the same in units of kelvin and degrees Celsius. Note that the total heat capacity C is simply the product of the specific estrus capacity c and the mass of the substance 1000, i.eastward.,

[latex]\text{C}=\text{mc}[/latex] or [latex]\text{c}=\frac{\text{C}}{\text{m}}=\frac{\text{C}}{\rho \text{Five}}[/latex],

where ϱ is the density of the substance and 5 is its book.

Values of specific oestrus must generally be looked up in tables, because there is no unproblematic way to calculate them. Instead, they are measured empirically. In general, the specific heat also depends on the temperature. The table below lists representative values of specific heat for diverse substances. Except for gases, the temperature and volume dependence of the specific heat of most substances is weak. The specific heat of water is v times that of drinking glass and ten times that of fe, which ways that it takes 5 times as much rut to heighten the temperature of water the aforementioned amount equally for drinking glass and 10 times as much heat to raise the temperature of water as for iron. In fact, water has one of the largest specific heats of any material, which is important for sustaining life on Earth.

Specific Heats: Listed are the specific heats of various substances. These values are identical in units of cal/(1000⋅C).3. cv at constant volume and at 20.0ºC, except equally noted, and at 1.00 atm average pressure level. Values in parentheses are cp at a constant pressure of 1.00 atm.

Calorimetry

Calorimetry is the measurement of the heat of chemical reactions or physical changes.

Learning Objectives

Analyze the relationship between the gas constant for an ideal gas yield and volume

Key Takeaways

Central Points

• A calorimeter is used to measure the heat generated (or absorbed) by a physical change or chemical reaction. The science of measuring these changes is known as calorimetry.
• In gild to do calorimetry, information technology is crucial to know the specific heats of the substances existence measured.
• Calorimetry can be performed under constant volume or constant pressure. The type of adding done depends on the weather condition of the experiment.

Key Terms

• abiding-pressure calorimeter: An instrument used to mensurate the heat generated during changes that exercise not involve changes in pressure level.
• calorimeter: An apparatus for measuring the heat generated or absorbed past either a chemical reaction, alter of phase or another concrete modify.
• constant-volume calorimeter: An instrument used to measure the heat generated during changes that practise not involve changes in volume.

Calorimetry

Overview

Calorimetry is the scientific discipline of measuring the heat of chemical reactions or physical changes. Calorimetry is performed with a calorimeter. A simple calorimeter just consists of a thermometer attached to a metal container full of water suspended above a combustion bedchamber. The discussion calorimetry is derived from the Latin word calor, pregnant oestrus. Scottish physician and scientist Joseph Black, who was the outset to recognize the distinction betwixt heat and temperature, is said to be the founder of calorimetry.

Calorimetry requires that the cloth existence heated have known thermal properties, i.eastward. specific heat capacities. The classical dominion, recognized by Clausius and by Kelvin, is that the pressure exerted by the calorimetric material is fully and speedily determined solely by its temperature and volume; this rule is for changes that practise not involve phase alter, such as melting of ice. There are many materials that practice not comply with this rule, and for them, more than complex equations are required than those beneath.

Ice Calorimeter: The world'due south first ice-calorimeter, used in the winter of 1782-83, by Antoine Lavoisier and Pierre-Simon Laplace, to determine the heat evolved in variouschemical changes; calculations which were based on Joseph Black's prior discovery of latent oestrus. These experiments mark the foundation of thermochemistry.

Basic Calorimetry at Constant Value

Abiding-volume calorimetry is calorimetry performed at a abiding book. This involves the employ of a constant-volume calorimeter (one blazon is called a Bomb calorimeter). For constant-volume calorimetry:

[latex]\delta \text{Q}=\text{C}_{\text{V}}\Delta \text{T}=\text{mc}_{\text{V}}\Delta \text{T}[/latex]

where δQ is the increment of heat gained by the sample, C_V is the oestrus capacity at constant volume, c_v is the specific heat at constant volume, and ΔT is the change in temperature.

Measuring Enthalpy Alter

To notice the enthalpy modify per mass (or per mole) of a substance A in a reaction between two substances A and B, the substances are added to a calorimeter and the initial and final temperatures (before the reaction started and after it has finished) are noted. Multiplying the temperature change past the mass and specific heat capacities of the substances gives a value for the energy given off or absorbed during the reaction:

[latex]\delta \text{Q}=\Delta \text{T}(\text{m}_{\text{A}}\text{c}_{\text{A}}+\text{m}_{\text{B}}\text{c}_{\text{B}})[/latex]

Dividing the free energy change by how many grams (or moles) of A were present gives its enthalpy change of reaction. This method is used primarily in bookish pedagogy as information technology describes the theory of calorimetry. It does not account for the heat loss through the container or the heat chapters of the thermometer and container itself. In add-on, the object placed within the calorimeter shows that the objects transferred their heat to the calorimeter and into the liquid, and the estrus absorbed by the calorimeter and the liquid is equal to the oestrus given off past the metals.

Constant-Pressure Calorimetry

A abiding-pressure calorimeter measures the alter in enthalpy of a reaction occurring in solution during which the atmospheric pressure level remains abiding. An instance is a java-cup calorimeter, which is constructed from two nested Styrofoam cups and a lid with ii holes, allowing insertion of a thermometer and a stirring rod. The inner cup holds a known amount of a solute, usually water, that absorbs the heat from the reaction. When the reaction occurs, the outer cup provides insulation. Then

[latex]\text{C}_{\text{P}}=\frac{\text{W}\Delta \text{H}}{\text{M}\Delta \text{T}}[/latex]

where C_p is the specific heat at constant pressure, ΔH is the enthalpy of the solution, ΔT is the modify in temperature, W is the mass of the solute, and M is the molecular mass of the solute. The measurement of heat using a simple calorimeter, like the java loving cup calorimeter, is an instance of constant-pressure level calorimetry, since the pressure (atmospheric pressure) remains constant during the process. Constant-force per unit area calorimetry is used in determining the changes in enthalpy occurring in solution. Under these weather condition the alter in enthalpy equals the heat (Q=ΔH).

Specific Oestrus for an Ideal Gas at Constant Pressure and Book

An ideal gas has different specific heat capacities under constant volume or abiding pressure conditions.

Learning Objectives

Explicate how to derive the adiabatic index

Key Takeaways

Cardinal Points

• The specific heat at abiding book for a gas is given equally [latex](\frac{\fractional \text{U}}{\fractional \text{T}})_{\text{Five}}=\text{c}_{\text{v}}[/latex].
• The specific heat at constant pressure for an ideal gas is given every bit [latex](\frac{\partial \text{H}}{\partial \text{T}})_{\text{Five}}=\text{c}_{\text{p}}=\text{c}_{\text{v}}+\text{R}[/latex].
• The heat chapters ratio (or adiabatic index ) is the ratio of the estrus chapters at abiding pressure level to rut capacity at abiding volume.

Key Terms

• Fundamental Thermodynamic Relation: In thermodynamics, the key thermodynamic relation expresses an infinitesimal change in internal energy in terms of infinitesimal changes in entropy, and volume for a airtight system in thermal equilibrium in the following mode: dU=TdS-PdV. Hither, U is internal energy, T is absolute temperature, Due south is entropy, P is pressure and V is volume.
• adiabatic index: The ratio of the heat chapters at abiding pressure to heat capacity at abiding volume.
• specific estrus: The ratio of the amount of heat needed to raise the temperature of a unit mass of substance past a unit caste to the corporeality of oestrus needed to raise that of the same mass of h2o by the same amount.

Specific Heat for an Platonic Gas at Constant Pressure and Volume

The rut capacity at abiding volume of nR = ane J·One thousand⁻¹ of whatsoever gas, including an ideal gas is:

[latex](\frac{\fractional \text{U}}{\partial \text{T}})_{\text{V}}=\text{c}_{\text{v}}[/latex]

This represents the dimensionless rut capacity at constant volume; it is mostly a part of temperature due to intermolecular forces. For moderate temperatures, the abiding for a monoatomic gas is c_five=iii/ii while for a diatomic gas it is c_v=5/2 (encounter ). Macroscopic measurements on estrus capacity provide information on the microscopic construction of the molecules.

Molecular internal vibrations: When a gas is heated, translational kientic energy of molecules in the gas will increase. In add-on, molecules in the gas may choice up many characteristic internal vibrations. Potential energy stored in these internal degrees of freedom contributes to specific heat of the gas.

The rut chapters at constant pressure of 1 J·1000⁻¹ ideal gas is:

[latex](\frac{\fractional \text{H}}{\fractional \text{T}})_{\text{Five}}=\text{c}_{\text{p}}=\text{c}_{\text{five}}+\text{R}[/latex]

where H=U+pV is the enthalpy of the gas.

Measuring the heat capacity at abiding volume tin be prohibitively hard for liquids and solids. That is, minor temperature changes typically require large pressures to maintain a liquid or solid at constant volume (this implies the containing vessel must exist nearly rigid or at least very strong). It is easier to measure the rut chapters at constant force per unit area (assuasive the fabric to expand or contract freely) and solve for the heat capacity at constant volume using mathematical relationships derived from the bones thermodynamic laws.

Utilizing the Fundamental Thermodynamic Relation nosotros can show:

[latex]\text{C}_{\text{p}}-\text{C}_{\text{V}}=\text{T}(\frac{\partial \text{P}}{\partial \text{T}})_{\text{5},\text{N}}(\frac{\fractional \text{Five}}{\fractional \text{T}})_{\text{p},\text{N}}[/latex]

where the partial derivatives are taken at: constant volume and abiding number of particles, and at abiding force per unit area and constant number of particles, respectively.

The estrus capacity ratio or adiabatic index is the ratio of the estrus capacity at constant pressure to heat capacity at constant book. It is sometimes also known as the isentropic expansion gene:

[latex]\gamma =\frac{\text{C}_{\text{P}}}{\text{C}_{\text{V}}}=\frac{\text{c}_{\text{p}}}{\text{c}_{\text{v}}}[/latex]

For an platonic gas, evaluating the partial derivatives above according to the equation of state, where R is the gas constant for an ideal gas yields:

[latex]\text{pV} = \text{RT}[/latex]

[latex]\text{C}_{\text{p}}-\text{C}_{\text{V}}=\text{T}(\frac{\partial \text{P}}{\partial \text{T}})_{\text{V}}(\frac{\fractional \text{V}}{\partial \text{T}})_{\text{p}}[/latex]

[latex]\text{C}_{\text{p}}-\text{C}_{\text{V}}=-\text{T}(\frac{\fractional \text{P}}{\partial \text{Five}})_{\text{5}}(\frac{\partial \text{5}}{\partial \text{T}})_{\text{p}}^{2}[/latex]

[latex]\text{P}=\frac{\text{RT}}{\text{V}}\text{n} \to (\frac{\partial \text{P}}{\partial \text{V}})_{\text{T}}=\frac{-\text{RT}}{\text{Five}^{ii}}=\frac{-\text{P}}{\text{Five}}[/latex]

[latex]\text{V}=\frac{\text{RT}}{\text{P}}\text{north} \to (\frac{\partial \text{V}}{\partial \text{T}})^{two}_{\text{p}}=\frac{\text{R}^{two}}{\text{P}^{2}}[/latex]

substituting:

[latex]-\text{T}(\frac{\partial \text{P}}{\partial \text{V}})_{\text{V}}(\frac{\partial \text{V}}{\partial \text{T}})_{\text{p}}^{ii}=-\text{T}\frac{-\text{P}}{\text{5}}\frac{\text{R}^{2}}{\text{P}^{ii}}=\text{R}[/latex]

This equation reduces merely to what is known equally Mayer's relation:

Julius Robert Mayer: Julius Robert von Mayer (Nov 25, 1814 – March 20, 1878), a German doctor and physicist, was one of the founders of thermodynamics. He is all-time known for his 1841 enunciation of one of the original statements of the conservation of energy (or what is now known as i of the first versions of the first law of thermodynamics): "Energy tin can exist neither created nor destroyed. " In 1842, Mayer described the vital chemical process now referred to equally oxidation as the primary source of energy for whatever living animal. His achievements were overlooked and credit for the discovery of the mechanical equivalent of heat was attributed to James Joule in the following year. von Mayer also proposed that plants convert light into chemic energy.

[latex]\text{C}_{\text{P}}-\text{C}_{\text{5}}=\text{R}[/latex].

Information technology is a elementary equation relating the heat capacities under abiding temperature and nether constant pressure level.

Solving Problems with Calorimetry

Calorimetry is used to measure the amount of heat produced or consumed in a chemical reaction.

Learning Objectives

Explain a bomb calorimeter is used to mensurate rut evolved in a combustion reaction

Key Takeaways

Primal Points

• Calorimetry is used to mensurate amounts of heat transferred to or from a substance.
• A calorimeter  is a device used to measure out the corporeality of heat involved in a chemical or physical process.
• This means that the amount of heat produced or consumed in the reaction equals the corporeality of heat absorbed or lost by the solution.

Fundamental Terms

• heat of reaction: The enthalpy change in a chemic reaction; the corporeality of estrus that a systems gives upward to its surroundings so information technology tin can return to its initial temperature.
• combustion: A procedure where two chemicals are combined to produce estrus.

Calorimeters are designed to minimize energy substitution betwixt the organization being studied and its surroundings. They range from unproblematic coffee loving cup calorimeters used past introductory chemical science students to sophisticated bomb calorimeters used to determine the energy content of food.

Calorimetry is used to measure amounts of estrus transferred to or from a substance. To do so, the estrus is exchanged with a calibrated object (calorimeter). The modify in temperature of the measuring part of the calorimeter is converted into the amount of estrus (since the previous scale was used to establish its heat capacity ). The measurement of heat transfer using this approach requires the definition of a system (the substance or substances undergoing the chemical or concrete change) and its surround (the other components of the measurement appliance that serve to either provide estrus to the system or absorb heat from the system). Noesis of the heat capacity of the environment, and careful measurements of the masses of the system and surroundings and their temperatures before and after the process allows i to calculate the heat transferred every bit described in this department.

A calorimeter is a device used to mensurate the amount of oestrus involved in a chemical or physical process. For example, when an exothermic reaction occurs in solution in a calorimeter, the heat produced by the reaction is captivated by the solution, which increases its temperature. When an endothermic reaction occurs, the heat required is absorbed from the thermal energy of the solution, which decreases its temperature. The temperature modify, along with the specific heat and mass of the solution, can so be used to calculate the amount of estrus involved in either case.

Coffee-Cup Calorimeters

Full general chemistry students ofttimes utilize simple calorimeters constructed from polystyrene cups. These piece of cake-to-use "coffee cup" calorimeters allow more heat exchange with their environment, and therefore produce less accurate energy values.

Structure of the Abiding Volume (or "Flop") Calorimeter

Bomb Calorimeter: This is the picture of a typical setup of bomb calorimeter.

A unlike blazon of calorimeter that operates at constant volume, colloquially known as a bomb calorimeter, is used to measure the energy produced past reactions that yield large amounts of estrus and gaseous products, such every bit combustion reactions. (The term "bomb" comes from the observation that these reactions tin be vigorous enough to resemble explosions that would harm other calorimeters.) This type of calorimeter consists of a robust steel container (the "bomb") that contains the reactants and is itself submerged in h2o. The sample is placed in the bomb, which is then filled with oxygen at high pressure. A minor electric spark is used to ignite the sample. The energy produced by the reaction is trapped in the steel bomb and the surrounding water. The temperature increase is measured and, forth with the known rut capacity of the calorimeter, is used to calculate the free energy produced past the reaction. Bomb calorimeters require scale to make up one's mind the heat capacity of the calorimeter and ensure accurate results. The calibration is accomplished using a reaction with a known q, such equally a measured quantity of benzoic acid ignited by a spark from a nickel fuse wire that is weighed before and afterward the reaction. The temperature change produced by the known reaction is used to determine the heat capacity of the calorimeter. The scale is generally performed each time earlier the calorimeter is used to get together research information.

Example: Identifying a Metal by Measuring Specific Heat

A 59.7 g piece of metal that had been submerged in boiling h2o was quickly transferred into sixty.0 mL of water initially at 22.0 °C. The final temperature is 28.five °C. Use these information to determine the specific rut of the metal. Use this consequence to identify the metallic.

Solution

Assuming perfect estrus transfer, the heat given off past metal is the negative of the rut taken in by water, or:

[latex]\text{q}_{\text{metal}}=-\text{q}_{\text{water}}[/latex]

In expanded form, this is:

[latex]\text{c}_{\text{metal}} \times \text{m}_{\text{metal}} \times \left( \text{T}_{\text{f,metal}}-\text{T}_{\text{i,metallic}} \right) = \text{c}_{\text{h2o}} \times \text{k}_{\text{h2o}} \times \left( \text{T}_{\text{f,water}}-\text{T}_{\text{i,h2o}} \right)[/latex]

Noting that since the metal was submerged in humid water, its initial temperature was 100.0 °C; and that for h2o, 60.0 mL = 60.0 g; we have:

[latex]\left( \text{c}_{\text{metal}} \correct)\left( 59.7\text{ g} \right)\left( 28.5^{\text{o}} \text{C} - 100.0^{\text{o}} \text{C} \right) = \left( iv.18 \text{ J/yard}^{\text{o}} \text{C} \correct) \left( 60.0\text{ k} \right)\left( 28.v^{\text{o}} \text{C} - 22.0^{\text{o}} \text{C} \right)[/latex]

Solving this:

[latex]\text{c}_{\text{metal}} = \dfrac{- \left( iv.184 \text{ J/g}^{\text{o}} \text{C} \right) \left( 60.0\text{ g} \right)\left( vi.five^{\text{o}} \text{C} \right)}{\left( 59.seven\text{ grand} \right)\left( -71.five^{\text{o}} \text{C} \correct)} = 0.38 \text{ J/k}^{\text{o}} \text{C} [/latex]

Our experimental specific estrus is closest to the value for copper (0.39 J/g °C), so we identify the metal as copper.

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Source: https://courses.lumenlearning.com/boundless-physics/chapter/specific-heat/

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