Laws of Thermodynamics & Heat Engine - Physics Class 11 - NEET

Zeroth Law of Thermodynamics:

According to this law, two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other. Thus, if A and B are separately in equilibrium with C, that is if T_A = T_C and T_B = T_C, then this implies that T_A = T_B i.e., the systems A and B are also in thermal equilibrium.

First Law of Thermodynamics:

Heat given to a thermodynamic system (ΔQ) is partially utilized in doing work (ΔW) against the surrounding and the remaining part increases the internal energy (ΔU) of the system.

Therefore, ΔQ = ΔU + ΔW

First law of thermodynamics is a restatement of the principle conservation of energy.

In an isothermal process, change in internal energy is zero (ΔU = 0).

Therefore, ΔQ = ΔW

In an adiabatic process, no exchange of heat takes place, i.e., Δθ = O.

Therefore, ΔU = – ΔW

In an adiabatic process, if gas expands, its internal energy and hence, temperature decreases and vice-versa.

In an isochoric process, work done is zero, i.e., ΔW = 0, therefore

ΔQ = ΔU

Thermodynamic Processes:

A thermodynamical process is said to take place when some changes occur in the state of a thermodynamic system i.e., the thermodynamic parameters of the system change with time.

(i) Isothermal Process:

A process taking place in a thermodynamic system at constant temperature is called an isothermal process.

Isothermal processes are very slow processes.

These process follows Boyle’s law, according to which

pV = constant

From dU = nC_vdT as dT = 0 so dU = 0, i.e., internal energy is constant.

From first law of thermodynamics, dQ = dW, i.e., heat given to the system is equal to the work done by system surroundings.

Work done W = 2.3026μRT l0g₁₀(V_f / V_i) = 2.3026μRT l0g₁₀(p_i / p_f)

where, μ = number of moles, R = ideal gas constant, T = absolute temperature and V_i V_f and P_i, P_f are initial volumes and pressures.

After differentiating P V = constant, we have

i.e., bulk modulus of gas in isothermal process, β = p.

P – V curve for this persons is a rectangular hyperbola

Examples:

(a) Melting process is an isothermal change, because temperature of a substance remains constant during melting.

(b) Boiling process is also an isothermal operation.

(ii) Adiabatic Process

A process taking place in a thermodynamic system for which there is no exchange of heat between the system and its surroundings.

Adiabatic processes are very fast processes.

These process follows Poisson’s law, according to which

From dQ = nCdT, C_adi = 0 as dQ = 0, i.e., molar heat capacity for adiabatic process is zero.

From first law, dU = – dW, i.e., work done by the system is equal to decrease in internal energy. When a system expands adiabatically, work done is positive and hence internal energy decrease, i.e., the system cools down and vice-versa.

Work done in an adiabatic process is

where T_i and T_f are initial and final temperatures. Examples

(a) Sudden compression or expansion of a gas in a container with perfectly non-conducting wall.

(b) Sudden bursting of the tube of a bicycle tyre.

(c) Propagation of sound waves in air and other gases.

(iii) Isobaric Process

A process taking place in a thermodynamic system at constant pressure is called an isobaric process.

Molar heat capacity of the process is C_p and dQ = nC_pdT.

Internal energy dU = nC_v dT

From the first law of thermodynamics
dQ = dU + dW
dW = pdV = nRdT

Process equation is V / T = constant.

p- V curve is a straight line parallel to volume axis.

(iv) Isochoric Process 

A process taking place in a thermodynamics system at constant volume is called an isochoric process.

dQ = nC_vdT, molar heat capacity for isochoric process is C_v.

Volume is constant, so dW = 0,

Process equation is p / T = constant

p- V curve is a straight line parallel to pressure axis.

(v) Cyclic Process 

When a thermodynamic system returns to the initial state after passing through several states, then it is called cyclic process.
Efficiency of the cycle is given by

Work done by the cycle can be computed from area enclosed cycle on p- V curve.

Isothermal and Adiabatic Curves

The graph drawn between the pressure p and the volume V of a given mass of a gas for an isothermal process is called isothermal curve and for an adiabatic process it is called adiabatic curve .

Fig: Isothermal vs adiabatic curve

The slope of the adiabatic curve

= γ x the slope of the isothermal curve

Volume Elasticities of Gases:

There are two types of volume elasticities of gases:

(i) Isothermal modulus of elasticity E_S = p

(ii) Adiabatic modulus of elasticity E_T = γ p

Ratio between isothermal and adiabatic modulus

E_S / E_T = γ = C_p / C_V

where C_p and C_v are specific heats of gas at constant pressure and at constant volume.

For an isothermal process Δt = 0, therefore specific heat,

c = Δ θ / m Δt = &;

For an adiabatic process 119= 0, therefore specific heat,

c = 0 / m Δt = 0

Second Law of Thermodynamics:

The second law of thermodynamics gives a fundamental limitation to the efficiency of a heat engine and the coefficient of performance of a refrigerator. It says that efficiency of a heat engine can never be unity (or 100%). This implies that heat released to the cold reservoir can never be made zero.

Kelvin’s Statement:

It is impossible to obtain a continuous supply of work from a body by cooling it to a temperature below the coldest of its surroundings.

Clausius’ Statement:

It is impossible to transfer heat from a lower temperature body to a higher temperature body without use of an external agency.

Planck’s Statement:

It is impossible to construct a heat engine that will convert heat completely into work.

All these statements are equivalent as one can be obtained from the other.

Entropy:

Entropy is a physical quantity that remains constant during a reversible adiabatic change.

Change in entropy is given by dS = δQ / T

Where, δQ = heat supplied to the system

and T = absolute temperature.

Entropy of a system never decreases, i.e., dS ≥ o.

Entropy of a system increases in an irreversible process

Heat Engine:

A heat energy engine is a device which converts heat energy into mechanical energy.

Fig: Heat Engine

A heat engine consists of three parts:

(i) Source of heat at higher temperature

(ii) Working substance

(iii) Sink of heat at lower temperature

Thermal efficiency of a heat engine is given by

where Q₁ is heat absorbed from the source,

Q₂ is heat rejected to the sink and T₁ and T₂ are temperatures of source and sink.

Heat engine are of two types:

(i) External Combustion Engine: In this engine fuel is burnt a chamber outside the main body of the engine. e.g., steam engine. In practical life thermal efficiency of a steam engine varies from 12% to 16%.

(ii) Internal Combustion Engine: In this engine, fuel is burnt inside the main body of the engine. e.g., petrol and diesel engine. In practical life thermal efficiency of a petrol engine is 26% and a diesel engine is 40%.