## Specific Heat and Heat Capacity

Heat capacity is a measure of the quantity of heat power required to adjust the temperature of a pure problem by a provided amount.

You are watching: What is the heat capacity of the unknown substance?

### Learning Objectives

Calculate the readjust in temperature the a substance offered its heat capacity and the energy used to warm it

### Key Takeaways

Key PointsHeat volume is the proportion of the quantity of heat power transferred to an object to the resulting increase in the temperature.Molar warmth capacity is a measure up of the quantity of heat essential to advanced the temperature that one mole of a pure substance by one degree K.Specific warm capacity is a measure of the quantity of heat important to raise the temperature the one gram the a pure substance by one level K.Key Termsheat capacity: The capability of a substance to absorb warm energy; the lot of heat forced to advanced the temperature of one mole or gram of a problem by one degree Celsius without any change of phase.specific heat capacity: The lot of warmth that have to be included or removed from a unit fixed of a problem to readjust its temperature by one Kelvin.

### Heat Capacity

Heat capacity is an intrinsic physical residential property of a substance that steps the quantity of heat forced to change that substance’s temperature through a given amount. In the global System of devices (SI), warmth capacity is express in units of joules per kelvin left(Jcdot K^-1 ight). Warmth capacity is substantial property, meaning that it is dependent top top the size/mass that the sample. For instance, a sample containing twice the lot of substance as another sample would call for twice the lot of heat power (Q) to attain the same readjust in temperature (Delta T) together that compelled to change the temperature the the first sample.

### Molar and particular Heat Capacities

There are two acquired quantities the specify warm capacity as an extensive property (i.e., live independence of the size of a sample) of a substance. They are:

the molar warm capacity, i m sorry is the warmth capacity per mole the a pure substance. Molar warm capacity is often designated CP, to represent heat volume under consistent pressure conditions, and CV, to signify heat capacity under consistent volume conditions. Systems of molar warmth capacity room fracJKcdot ext mol.the certain heat capacity, frequently simply called particular heat, which is the warmth capacity per unit mass of a pure substance. This is designated cP and also cV and its devices are provided in fracJgcdot K.

### Heat, Enthalpy, and Temperature

Given the molar heat capacity or the certain heat for a pure substance, the is feasible to calculate the amount of heat required to raise/lower the substance’s temperature through a offered amount. The complying with two formulas apply:

q=mc_pDelta T

q=nC_PDelta T

In this equations, m is the substance’s fixed in grams (used once calculating with specific heat), and also n is the number of moles of problem (used when calculating through molar warm capacity).

### Example

The molar warm capacity that water, CP, is 75.2fracJ extmolcdot K. How much warmth is compelled to advanced the temperature the 36 grams the water indigenous 300 come 310 K?

We are provided the molar heat capacity of water, for this reason we require to transform the offered mass of water come moles:

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

Now we deserve to plug our values into the formula the relates heat and also 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 used to measure up the change in internal energy, Delta U, the a reaction. At continuous volume, this is same to qV, the warm of reaction.The calorimeter has actually its own warmth capacity, which have to be accounted for once doing calculations.Key Termsbomb calorimeter: A bomb calorimeter is a kind of constant-volume calorimeter used in measuring the warm of burning of a details reaction.calorie: The quantity of energy needed come raise the temperature the 1 gram of water by 1 °C. That 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 provided to measure the warm that a reaction absorbs or releases, and is practically used to measure up the calorie contents of food. A bomb calorimeter is a form of constant-volume calorimeter used to measure up a details reaction’s heat of combustion. For instance, if we were interested in identify the heat content the a episode roll, for example, we would certainly be feather to uncover out the number of calories the contains. In stimulate to do this, us would location the sushi roll in a container referred to as the “bomb”, seal it, and then immerse the in the water within the calorimeter. Then, we would certainly evacuate every the air out of the bomb before pumping in pure oxygen gas (O2). After the oxygen is added, a fuse would certainly ignite the sample leading to it to combust, thereby yielding carbon dioxide, gas water, and also heat. Together such, bomb calorimeters are built to withstand the big pressures created from the gaseous commodities in these burning reactions.

Bomb calorimeter: A schematic depiction of a bomb calorimeter used for the measure of heats the combustion. The weighed sample is inserted in a crucible, which subsequently is placed in the bomb. The sample is burned fully in oxygen under pressure. The sample is ignited by one iron wire ignition coil the glows once heated. The calorimeter is filled through fluid, usually water, and insulated by method of a jacket. The temperature that the water is measured through the thermometer. Native the change in temperature, the warmth of reaction deserve to be calculated.

Once the sample is totally combusted, the warm released in the reaction move to the water and the calorimeter. The temperature readjust of the water is measured with a thermometer. The total heat provided off in the reaction will certainly be same to the heat obtained by the water and the calorimeter:

q_rxn=-q_cal

Keep in mind the the heat got by the calorimeter is the amount of the heat obtained by the water, as well as the calorimeter itself. This have the right to be expressed together 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 warmth capacity that the calorimeter (typically in frac extcal^circ extC). Therefore, as soon as running bomb calorimetry experiments, it is important to calibrate the calorimeter in bespeak to determine Ccal.

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

ΔU=qV

where ΔU is the adjust in inner energy, and qV denotes the heat absorbed or released by the reaction measure up under conditions of constant volume. (This expression was previously derived in the “Internal Energy and also Enthalpy ” section.) Thus, the total heat provided off by the reaction is concerned the adjust in internal power (ΔU), not the readjust in enthalpy (ΔH) i beg your pardon is measure under problems of constant pressure.

The value produced by together experiments walk not completely reflect exactly how our human body burns food. Because that example, we cannot digest fiber, so derived values need to be repair to account for such differences in between experimental (total) and actual (what the human body can absorb) values.

## Constant-Pressure Calorimetry

A constant-pressure calorimeter measures the change in enthalpy of a reaction at constant pressure.

### Learning Objectives

Discuss just how a constant-pressure calorimeter works

### Key Takeaways

Key PointsA constant- push calorimeter steps the readjust in enthalpy ( Delta H ) of a reaction arising in solution, during which the push remains constant. Under these conditions, the adjust in enthalpy the the reaction is equal to the measure up heat.Change in enthalpy have the right to be calculated based on the readjust in temperature of the solution, its certain heat capacity, and also mass.Key Termsconstant-pressure calorimeter: procedures the change in enthalpy the a reaction developing in solution, during which the push remains constant.adiabatic: Not enabling any deliver of warmth energy; perfectly insulating.coffee-cup calorimeter: an instance of constant-pressure calorimeter.

### Constant-Pressure Calorimetry

A constant-pressure calorimeter steps the adjust in enthalpy that a reaction occurring in a liquid solution. In that case, the gas pressure above the solution stays constant, and we say that the reaction is occurring under conditions of consistent pressure. The heat transferred to/from the equipment in order because that the reaction to occur is equal to the adjust in enthalpy (Delta H = q_P), and a constant-pressure calorimeter for this reason measures this heat of reaction. In contrast, a bomb calorimeter ‘s volume is constant, so over there is no pressure-volume work and also the warmth measured relates come the change in internal energy (Delta U=q_V).

A basic example the a constant-pressure calorimeter is a coffee-cup calorimeter, i beg your pardon is built from two nested Styrofoam cups and also a lid through two holes, which enables for the insertion the a thermometer and also a stirring rod. The within cup hold a known amount of a liquid, normally water, the absorbs the heat from the reaction. The outer cup is assumed to be perfectly adiabatic, meaning that it does not absorb any kind of heat whatsoever. Together such, the external cup is presume to be a perfect insulator. Coffee cup calorimeter: A styrofoam cup v an placed thermometer can be supplied as a calorimeter, in stimulate to measure the adjust in enthalpy/heat that reaction at continuous pressure.

### Calculating particular Heat

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

q=mCDelta T

We will currently illustrate exactly how to use this equation to calculation the details heat capacity of a substance.

### Example 1

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

The wall surfaces of the coffee-cup calorimeter room assumed come be perfect adiabatic, for this reason we deserve to assume that all of the warm 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 have the right to plug in our known 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 details heat capacity of the unknown steel is 0.166 frac J g ^circ extC.

### Example 2

To recognize the traditional enthalpy that the reaction H+(aq) + OH–(aq) → H2O(l), equal volumes of 0.1 M solutions of HCl and of NaOH deserve to be merged initially in ~ 25°C.

See more: Which Of The Following Molecules Has A Trigonal Pyramidal Shape ?

This process is exothermic and as a result, a specific amount of warm qP will certainly be released right into the solution. The variety of joules of warmth released right into each gram that the systems is calculated indigenous the product the the climb in temperature and the certain heat volume of water (assuming the the systems is dilute sufficient so the its specific heat capacity is the same as that of pure water’s). The full quantity of transferred heat deserve to then be calculated by multiply the an outcome with the fixed of the solution.