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Thermo Chemistry / Thermo Dynamics

How to Measure Heat Flow & Enthalpy Change


A calorimeter is a device that is used to measure the quantity of heat flow in a chemical reaction. Two common types of calorimeters are the coffee cup calorimeter and the bomb calorimeter.

Coffee Cup Calorimeter

A coffee cup calorimeter is essentially a polystyrene (Styrofoam) cup with a lid. Really, any well-insulated container will work. The cup is partially filled with a known volume of water and a thermometer is inserted through the lid of the cup so that the thermometer bulb is below the water surface. The water absorbs the heat of any chemical reaction taking place in the calorimeter. The change in the water temperature is used to calculate the amount of heat that has been absorbed (used to make products, so water temperature decreases) or evolved (lost to the water, so its temperature increases) in the reaction.

Heat flow is calculated using the relation:

q = Cp  .  m  . Dt

where q is heat flow, m is mass in grams, and Dt is the change in temperature in C. The specific heat Cpis the amount of heat required to raise the temperature of 1 gram of a substance 1 degree Celsius.

The specific heat of (pure) water is 4.186 J/(gC).

For example, consider a chemical reaction which occurs in 200 grams of water with an initial temperature of 25.0C. The reaction is allowed to proceed in the coffee cup calorimeter. As a result of the reaction, the temperature of the water changes to 31.0C. The heat flow is calculated:

qwater = 4.186 J/(gC) . 200 g . (31.0C - 25.0C)

qwater = +5.0 x 103 J

In other words, the products of the reaction evolved 5000 J of heat, which was lost to the water. The enthalpy change, DH, for the reaction is equal in magnitude but opposite in sign to the heat flow for the water:

DHreaction = -(qwater)

For an exothermic reaction, DH < 0; qwater is positive. The water absorbs heat from the reaction and an increase in temperature is seen. For an endothermic reaction, DH > 0; qwater is negative. The water supplies heat for the reaction and a decrease in temperature is seen.

Bomb Calorimeter

A coffee cup calorimeter is great for measuring heat flow in a solution, but it can't be used for reactions which involve gases, since they would escape from the cup. Also, a coffee cup calorimeter can't be used for high temperature reactions, since high heat would melt the cup. A bomb calorimeter is used to measure heat flows for gases and high temperature reactions.

A bomb calorimeter works the same way as a coffee cup calorimeter, with one big difference. In a coffee cup calorimeter, the reaction takes place in the water. In a bomb calorimeter, the reaction takes place in a sealed metal container, which is placed in the water in an insulated container. Heat flow from the reaction crosses the walls of the sealed container to the water. The temperature difference of the water is measured, just as it was for a coffee cup calorimeter. Analysis of the heat flow is a bit more complex than it was for the coffee cup calorimeter because the heat flow into the metal parts of the calorimeter must be taken into account:

qreaction = - (qwater + qbomb)

where qwater = 4.18 J/(gC) . mwater . Dt

The bomb has a fixed mass and specific heat. The mass of the bomb multiplied by its specific heat is sometimes termed the calorimeter constant, denoted by the symbol C with units of joules per degree Celsius. The calorimeter constant is determined experimentally and will vary from one calorimeter to the next. The heat flow of the bomb is:

qbomb = C . Dt

Once the calorimeter constant is known, calculating heat flow is a simple matter. The pressure within a bomb calorimeter often changes during a reaction, so the heat flow may not be equal in magnitude to the enthalpy change.

 

First Law of Thermodynamics

The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes:

The first law makes use of the key concepts of internal energy, heat, and system work. It is used extensively in the discussion of heat engines.

It is typical for chemistry texts to write the first law as ΔU=Q+W. It is the same law, of course - the thermodynamic expression of the conservation of energy principle. It is just that W is defined as the work done on the system instead of work done by the system. In the context of physics, the common scenario is one of adding heat to a volume of gas and using the expansion of that gas to do work, as in the pushing down of a piston in an internal combustion engine. In the context of chemical reactions and process, it may be more common to deal with situations where work is done on the system rather than by it.

Enthalpy

Four quantities called "thermodynamic potentials" are useful in the chemical thermodynamics of reactions and non-cyclic processes. They are internal energy, the enthalpy, the Helmholtz free energy and the Gibbs free energy. Enthalpy is defined by

H = U + PV

where P and V are the pressure and volume, and U is internal energy. Enthalpy is then a precisely measurable state variable, since it is defined in terms of three other precisely definable state variables. It is somewhat parallel to the first law of thermodynamics for a constant pressure system

Q = ΔU + PΔV since in this case Q=ΔH


It is a useful quantity for tracking chemical reactions. If as a result of an exothermic reaction some energy is released to a system, it has to show up in some measurable form in terms of the state variables. An increase in the enthalpy H = U + PV might be associated with an increase in internal energy which could be measured by calorimetric, or with work done by the system, or a combination of the two.

The internal energy U might be thought of as the energy required to create a system in the absence of changes in temperature or volume. But if the process changes the volume, as in a chemical reaction which produces a gaseous product, then work must be done to produce the change in volume. For a constant pressure process the work you must do to produce a volume change ΔV is PΔV. Then the term PV can be interpreted as the work you must do to "create room" for the system if you presume it started at zero volume.

 

System Work

When work is done by a thermodynamic system, it is usually a gas that is doing the work. The work done by a gas at constant pressure is:

Example

 

 

For non-constant pressure, the work can be visualized as the area under the pressure-volume curve which represents the process taking place. The more general expression for work done is:

 

Work done by a system decreases the internal energy of the system, as indicated in the First Law of Thermodynamics. System work is a major focus in the discussion of heat engines.

 

A More General View of Temperature

When a high temperature object is placed in contact with a low temperature object, then energy will flow from the high temperature object to the lower temperature object, and they will approach an equilibrium temperature. When the details of this common-sense scenario are examined, it becomes evident that the simple view of temperature embodied in the commonly used kinetic temperature approach has some significant problems.

The above illustration summarizes the situation when the kinetic temperature gives a reasonable general description of the nature of temperature. For monoatomic gases acting like point masses, a higher temperature simply implies higher average kinetic energy. Faster molecules striking slower ones at the boundary in elastic collisions will increase the velocity of the slower ones and decrease the velocity of the faster ones, transferring energy from the higher temperature to the lower temperature region. With time, the molecules in the two regions approach the same average kinetic energy (same temperature) and in this condition of thermal equilibrium there is no longer any net transfer of energy from one object to the other.

The concept of temperature is complicated by internal degrees of freedom like molecular rotation and vibration and by the existence of internal interactions in solid materials which can include collective modes. The internal motions of molecules affect the specific heats of gases, with diatomic hydrogen being the classic case. Collective modes affect the specific heats of solids, particularly at low temperatures.

Complications such as these have led to the adoption of a different approach to the concept of temperature in the study of thermodynamics. Schroeder's proposal for a theoretical definition of temperature is:

  • "Temperature is a measure of the tendency of an object to spontaneously give up energy to its surroundings. When two objects are in thermal contact, the one that tends to spontaneously lose energy is at the higher temperature, one loses and another one gains."

The kinetic temperature for monoatomic ideal gases described above is consistent with this definition of temperature for the simple systems to which it applies. In that case the equilibrium reached is one of maximum entropy, and the rate of approach to that state will be proportional to the difference in temperature between the two parts of the system. Noting that the equilibrium state of a collection of particles will be the state of greatest multiplicity, then one can define the temperature in terms of that multiplicity (entropy) as follows:

Temperature is expressed as the inverse of the rate of change of entropy with internal energy, with volume V and number of particles N held constant. This is certainly not as intuitive as molecular kinetic energy, but in thermodynamic applications it is more reliable and more general.

 

Specific Heat Capacities Table


Substance

J/g/oC
or J/g/K

cal/g/oC
or cal/g/K

Water (0 oC to 100 oC)

4.186

1.000

Methyl Alcohol

2.549

0.609

Ice (-10 oC to 0 oC)

2.093

0.500

Steam (100 oC)

2.009

0.480

Benzene

1.750

0.418

Wood (typical)

1.674

0.400

Soil (typical)

1.046

0.250

Air (50 oC)

1.046

0.250

Aluminum

0.900

0.215

Marble

0.858

0.205

Glass (typical)

0.837

0.200

Iron/Steel

0.452

0.108

Copper

0.387

0.0924

Silver

0.236

0.0564

Mercury

0.138

0.0330

Gold

0.130

0.0310

Lead

0.128

0.0305

Values are at Room Temperature and Atmospheric Pressure unless otherwise stated.

 

SPECIFIC HEAT HOMEWORK PROBLEMS:


1) When a 50.0 gram piece of nickel absorbs 350.0 J of heat, the temperature of the nickel changes from 20.0 0C to 36.0 0C. What is the specific heat of nickel?

2) A solar-heating specialist is considering paraffin as a possible solar-heat collector. How many kilograms of paraffin would be needed to collect as much energy as 4.78 x 103 kg of water? The specific heat of paraffin is 2.9 J / g 0C. (Hint: Assume the same temperature change.)

3) Calculate the quantity of heat that must be removed from 200.0 grams of ethyl alcohol, C2H6O to cool it from 25.0 0C to 10.0 0C. (ethyl alcohol = 2.45 J / g 0C)

4) How much energy is required to heat a #10 iron nail with a mass of 7.0 grams from 25.0 0C until it becomes red hot at 750 0C?

5) If 5750 J of energy are added to a 455 gram piece of granite at 24.0 0C, what is the final temperature of the granite?

6) A 30.0 gram sample of an unknown metal is heated from 22.0 0C to 59.2 0C. During the process, 1.00 kJ of energy is absorbed by the metal. What is the specific heat of the metal?


SPECIFIC HEAT PRACTICE ANSWERS:

1) 0.438 J / g 0C

2) 6.9 x 103 kg paraffin

3) 7350 J or 7.35 kJ

4) 2.3 kJ

5) 39.7 0C

6) 0.896 J / g 0C

 

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