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‘Heat, Calorimetry and Thermodynamics by Aditya Abeysinghe’

Thermodynamics

Laws of thermodynamics

1. Zeroth law of thermodynamics If two systems are at the same time in equilibrium with a third system, they are in equilibrium with each other.Practically, this means that all three systems are at the same temperature.

AB

C

Since A and B are at equilibrium and B and C are at equilibrium, A and C are also at equilibrium according to the zeroth law

2. First law of thermodynamics The change in internal energy of a system is equal to the heat added to the system minus the work done by the system.dU = δQ – δW (U- internal energy of the system, Q-heat added to the system, W- work done by the system)The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes.

3. Second law of thermodynamicsWhen two initially isolated systems which are at thermal equilibriums are brought into contact they reach a common thermal equilibriumHowever, the second law can also be expressed in terms of the application in which it is used.For example,I. Second law in terms of heat flow: Heat flows spontaneously from hotter to colder objects but not vice versa.II. Second law in terms of heat engines: It is impossible to construct an engine which has 100% efficiency or a system in which the heat added to the system is solely used to perform work.

4. Third law of thermodynamicsThe entropy of a system approaches a constant value as the temperature approaches zero.

Second law: Heat engines

Kelvin-Planck statement:It is impossible to extract an amount of heat QH from a hot reservoir and use it all to do work W. Some amount of heat QC must be exhausted to a cold reservoir.

Refrigerator and Air Conditioner-Clausius Statement-It is impossible for heat to flow from a cold body to a warm body without any work ( or without the aid of an external agency) having been done to accomplish the flow.

W

QH

QC

Cold Reservoir

Hot Reservoir

Basics of Thermodynamics

Internal energy of a gas-The internal energy of a gas is the kinetic energy of thermal motion of its molecules.

Important:When a cylinder of a gas is moving in a locomotive or any other moving agent, the molecules inside the cylinder move relative to that of the cylinder (molecules travel in the same speed as the cylinder). Thus the kinetic energy of each molecule is equivalent to the kinetic energy experienced by the cylinder. Therefore, the temperature and thus the internal energy of the molecules relative to the cylinder is unchanged.

Deriving an equation for internal energy of a gas

The internal energy of a gas is the sum of the kinetic energy of the molecules and the potential energy(due to intermolecular attractions) between molecules.But there are no intermolecular forces between molecules in an ideal gas. Therefore, potential energy in such an instance is zero.Therefore, Internal Energy = Kinetic Energy of molecules

But, PV = ⅓ mNc2 and E = ½mNc2

So, PV = ⅓ × 2 × ½ mNc2

ETherefore, PV = ⅔E or, E= PV

But, PV = nRT . Therefore, E= nRTNow that E = ΔU,For a difference of temperature,Internal Energy = nRΔT (ΔU)

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Work done by gas-Work done by gas is the work done to increase its volume during expansion.

Δ W = FxΔ W = PAxTherefore, Δ W = P(ΔV)

P

A

F(PA)

X

Specific heats of a gas

When heat is given to a substance it expands and does external work. In the case of solids and liquids the change in volume and hence the external work done is negligible. Therefore, there is only one specific heat for a substance.Gases experience the effect of the change of volume to a great extent. Since the volume can be controlled, gases can be used to do variable amounts of external work. Therefore, there are no. of specific heats that can be defined for a gas.

The two most commonly used are-1. Specific heat at constant volume (CV)

It is the amount of heat required to raise the temperature of unit mass of a gas through 1°C, when volume is kept constant.

2. Specific heat at constant pressure (CP) It is the amount of heat required to raise the temperature of unit mass of a gas through 1°C, when the pressure of the gas is kept constant

However, CP > CV and CP / CV = γ. γ is called the ratio of specific heats.At constant volume, ΔQ = n CV θ

At constant pressure, ΔQ = n CP θ

The features of basic thermodynamic equations

ΔQ ΔU ΔWPositive

ORIncreasing

If heat is given from

outside

If internal energy

increases

If a gas does work to outside

Negative OR

Decreasing If heat is released

to outside

If internal energy

decreases

If work is done on the gas

ΔU

Increase / Decrease

Term

Special Occasions1. Isothermal Process (ΔU = 0) This usually occurs when a system is in thermal contact with a reservoir. The change occurs very slowly and the system will continually adjust to the temperature of the reservoir through heat exchange.ΔT = 0, therefore, ΔU = 0.Thus, ΔQ = ΔWThe graph of such a process is as follows:

P

V

Temperature constant. Therefore the system obeys Boyle’s Law

2. Adiabatic Process (ΔQ = 0) An expansion in which no heat energy enters or leaves the system.Adiabatic processes can take place if the container in which the process takes place has thermally-insulated walls or the process happens in an extremely short time.

Adiabatic Cooling- Occurs when the pressure of a substance is decreased as it does work on the surroundings

Adiabatic Heating-Occurs when the pressure of a gas is increased from work done on it by the surroundings.

The graph of such a process is as follows:

V

PA (T1)

B (T2)

Isothermal Processes

Adiabatic process

Each adiabat intersects each isotherm exactly once

An adiabat is similar to an isotherm, except that during expansion an adiabat loses more pressure than an isotherm, so it has a steeper inclination

Density of isotherms stays constant but the density of adiabats grow

3. Isochoric Process (ΔW = 0) Also called constant-volume process, iso volumetric process, and isometric process.Is a thermodynamic process during which the volume of the closed system stays constant.Since the system undergoes isochoric process, the volume is constant.Therefore,Q= mCv ΔT and Q = U (W=0)

The graph for such a process is as follows:

and since V is constant T

Other Processes1. Isobaric Process (Pressure Constant)

2. Isoentropic process (Entropy of system stays constant)