## Specific Heat and Heat Capacity

Heat volume is a measure of the amount of heat energy required to adjust the temperature the a pure substance by a given amount.

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### Learning Objectives

Calculate the readjust in temperature the a substance offered its warmth capacity and also the power used to warm it

### Key Takeaways

Key PointsHeat volume is the proportion of the quantity of heat power transferred to an item to the resulting boost in that temperature.Molar heat capacity is a measure of the amount of heat vital to progressive the temperature of one mole of a pure problem by one degree K.Specific heat capacity is a measure of the quantity of heat crucial to raise the temperature that one gram the a pure problem by one level K.Key Termsheat capacity: The capability of a problem to absorb warmth energy; the amount of heat compelled to progressive the temperature that one mole or gram the a problem by one degree Celsius there is no any adjust of phase.specific heat capacity: The quantity of warm that need to be added or removed from a unit fixed of a substance to change its temperature by one Kelvin.

### Heat Capacity

Heat volume is an intrinsic physical home of a substance that measures the quantity of heat compelled to readjust that substance’s temperature by a provided amount. In the global System of systems (SI), warm capacity is to express in units of joules per kelvin left(Jcdot K^-1 ight). Heat capacity is an extensive property, definition that it is dependent upon the size/mass that the sample. For instance, a sample containing twice the quantity of problem as an additional sample would need twice the lot of heat power (Q) to achieve the same adjust in temperature (Delta T) together that forced to readjust the temperature the the very first sample.

### Molar and details Heat Capacities

There are two acquired quantities the specify warm capacity together an intensive property (i.e., elevation of the size of a sample) that a substance. Lock are:

the molar heat capacity, i beg your pardon is the warm capacity per mole the a pure substance. Molar heat capacity is regularly designated CP, to denote heat volume under constant pressure conditions, as well as CV, to signify heat capacity under consistent volume conditions. Systems of molar heat capacity room fracJKcdot ext mol.the particular heat capacity, frequently simply called specific heat, i m sorry is the warm capacity per unit massive of a pure substance. This is designated cP and also cV and its devices are provided in fracJgcdot K.

### Heat, Enthalpy, and also Temperature

Given the molar warm capacity or the details heat because that a pure substance, it is feasible to calculate the amount of heat required to raise/lower the substance’s temperature through a provided amount. The complying with two formulas apply:

q=mc_pDelta T

q=nC_PDelta T

In these equations, m is the substance’s fixed in grams (used as soon as calculating with details heat), and also n is the number of moles of problem (used as soon as calculating through molar warmth capacity).

### Example

The molar warm capacity the water, CP, is 75.2fracJ extmolcdot K. Just how much heat is compelled to progressive the temperature that 36 grams the water indigenous 300 to 310 K?

We are provided the molar warmth capacity the water, so we need to convert the provided mass of water to moles:

ext36 grams imes frac ext1 mol extH_2 extO ext18 g= ext2.0 mol H_2 extO

Now we have the right to plug our values right into the formula the relates heat and heat capacity:

q=nC_PDelta T

q=(2.0; extmol)left(75.2;fracJ extmolcdot K ight)(10;K)

q=1504;J

### Key Takeaways

Key PointsA bomb calorimeter is supplied to measure the adjust in internal energy, Delta U, of a reaction. At constant volume, this is same to qV, the warmth of reaction.The calorimeter has actually its own warmth capacity, which have to be accounted for when doing calculations.Key Termsbomb calorimeter: A bomb calorimeter is a form of constant-volume calorimeter used in measure the heat of combustion of a particular reaction.calorie: The quantity of power needed come raise the temperature of 1 gram that water by 1 °C. It is a non-SI unit of energy equivalent to around 4.18 Joules. A Calorie (with a capital C) = 1000 calories.

### The Bomb Calorimeter

Bomb calorimetry is used to measure the heat that a reaction absorbs or releases, and also is virtually used to measure up the calorie content of food. A bomb calorimeter is a kind of constant-volume calorimeter offered to measure up a particular reaction’s heat of combustion. For instance, if us were interested in determining the warmth content the a sushi roll, for example, we would certainly be looking to find out the number of calories that contains. In bespeak to carry out this, we would place the sushi roll in a container described as the “bomb”, seal it, and also then immerse the in the water within the calorimeter. Then, we would certainly evacuate every the air out of the bomb prior to pumping in pure oxygen gas (O2). After the oxygen is added, a fuse would ignite the sample resulting in it come combust, thereby yielding carbon dioxide, gas water, and heat. Together such, bomb calorimeters are constructed to resist the huge pressures created from the gaseous products in these combustion reactions.

Bomb calorimeter: A schematic depiction of a bomb calorimeter used for the measure of heats that combustion. The sweet sample is placed in a crucible, which subsequently is inserted in the bomb. The sample is burned fully in oxygen under pressure. The sample is ignited by an iron cable ignition coil the glows when heated. The calorimeter is filled through fluid, generally water, and insulated by way of a jacket. The temperature that the water is measured with the thermometer. Native the readjust in temperature, the warm of reaction have the right to be calculated.

Once the sample is totally combusted, the warm released in the reaction move to the water and also the calorimeter. The temperature adjust of the water is measured with a thermometer. The total heat offered off in the reaction will be equal to the heat acquired by the water and the calorimeter:

q_rxn=-q_cal

Keep in mind the the heat obtained by the calorimeter is the amount of the heat obtained by the water, as well as the calorimeter itself. This deserve to be expressed as follows:

q_cal=m_ extwaterC_ extwaterDelta T+C_calDelta T

where Cwater denotes the specific heat volume of the water left(1 frac extcal extg ^circ extC ight), and Ccal is the warm capacity that the calorimeter (typically in frac extcal^circ extC). Therefore, when running bomb calorimetry experiments, that is vital to calibrate the calorimeter in stimulate to determine Ccal.

Since the volume is constant for a bomb calorimeter, over there is no pressure-volume work. As a result:

ΔU=qV

where ΔU is the adjust in internal energy, and qV denotes the heat soaked up or exit by the reaction measured under conditions of constant volume. (This expression was previously derived in the “Internal Energy and also Enthalpy ” section.) Thus, the full heat offered off through the reaction is concerned the change in internal power (ΔU), not the adjust in enthalpy (ΔH) i beg your pardon is measured under problems of constant pressure.

The value produced by together experiments walk not totally reflect exactly how our body burns food. For example, we cannot digest fiber, so derived values need to be corrected to account for such differences between experimental (total) and actual (what the person body deserve to absorb) values.

## Constant-Pressure Calorimetry

A constant-pressure calorimeter actions the adjust in enthalpy of a reaction at constant pressure.

### Learning Objectives

Discuss how a constant-pressure calorimeter works

### Key Takeaways

Key PointsA constant- press calorimeter procedures the change in enthalpy ( Delta H ) the a reaction emerging in solution, throughout which the press remains constant. Under these conditions, the change in enthalpy of the reaction is equal to the measure up heat.Change in enthalpy can be calculated based upon the change in temperature of the solution, its specific heat capacity, and also mass.Key Termsconstant-pressure calorimeter: procedures the change in enthalpy the a reaction arising in solution, throughout which the push remains constant.adiabatic: Not allowing any carry of warmth energy; perfect insulating.coffee-cup calorimeter: an instance of constant-pressure calorimeter.

### Constant-Pressure Calorimetry

A constant-pressure calorimeter actions the change in enthalpy of a reaction occurring in a fluid solution. In that case, the gaseous pressure over the solution stays constant, and also we say the the reaction is emerging under conditions of consistent pressure. The warm transferred to/from the equipment in order because that the reaction to happen is same to the change in enthalpy (Delta H = q_P), and also a constant-pressure calorimeter thus measures this warmth of reaction. In contrast, a bomb calorimeter ‘s volume is constant, so there is no pressure-volume work and also the warm measured relates come the change in internal energy (Delta U=q_V).

A straightforward example that a constant-pressure calorimeter is a coffee-cup calorimeter, i m sorry is created from 2 nested Styrofoam cups and a lid v two holes, which allows for the insertion of a thermometer and also a stirring rod. The inside cup holds a recognized amount that a liquid, normally water, that absorbs the warmth from the reaction. The external cup is assumed come be perfectly adiabatic, meaning that the does not absorb any type of heat whatsoever. As such, the outer cup is suspect to it is in a perfect insulator.

Coffee cup calorimeter: A styrofoam cup v an put thermometer have the right to be supplied as a calorimeter, in stimulate to measure up the change in enthalpy/heat of reaction at consistent pressure.

### Calculating particular Heat

Data built up during a constant-pressure calorimetry experiment deserve to be offered to calculate the warmth capacity of an unknown substance. We currently know our equation relating heat (q), particular heat capacity (C), and also the readjust in observed temperature (Delta T):

q=mCDelta T

We will now illustrate exactly how to usage this equation to calculate the details heat volume of a substance.

### Example 1

A college student heats a 5.0 g sample of one unknown metal to a temperature that 207 ^circC, and then fall the sample into a coffee-cup calorimeter comprise 36.0 g the water at 25.0 ^circC. After heat equilibrium has been established, the last temperature of the water in the calorimeter is 26.0^circC. What is the particular heat the the unknown metal? (The details heat the water is 4.18 frac J g^circ C)

The walls of the coffee-cup calorimeter space assumed to be perfect adiabatic, therefore we can assume that all of the warmth from the metal was moved to the water:

-q_ extmetal=q_ extwater

Substituting in our over equation, we get:

-m_ extmetalC_ extmetal Delta T_ extmetal=m_ extwaterC_ extwaterDelta T_ extwater

Then we deserve to plug in our recognized values:

-(5.0 ext g)C_ extmetal(26.0^circ extC-207^circ extC)=(36.0 ext g)(4.18; frac J extg^circ extC)(26.0^circ extC-25.0^circ extC)

Solving for C_ extmetal, us obtain

C_metal=0.166; frac J g^circ extC

The particular heat capacity of the unknown steel is 0.166 frac J g ^circ extC.

### Example 2

To identify the conventional enthalpy the the reaction H+(aq) + OH–(aq) → H2O(l), equal quantities of 0.1 M remedies of HCl and of NaOH deserve to be combined initially in ~ 25°C.

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This procedure is exothermic and as a result, a particular amount of heat qP will be released into the solution. The variety of joules of warm released into each gram that the equipment is calculated indigenous the product that the increase in temperature and the specific heat volume of water (assuming the the equipment is dilute sufficient so the its details heat capacity is the exact same as that of pure water’s). The full quantity of transferred heat have the right to then be calculated by multiply the an outcome with the mass of the solution.