Question

Explain different stages of Carnot's cycle with P-V-diagram.

Answer 1

When the Carnot engine works, the working substance of the engine goes through a different cycle known as the Carnot cycle, and this cycle consists of four different stages.

1. First stage (called isothermal expansion)

In this stroke, the barrel is placed over the source. The piston is gradually pushed back as the gas expands. Fall of temperature, due to expansion, is compensated by the supply of heat from the source, and consequently, the temperature remains constant. The conditions of the gas change from A(P₁, V₁) to B(P₂, V₂). If W₁ is the work done during this process, then heat Q₁, derived from the source is given by

W1 = -nRT₁ loge(V₂ / V₁)

2. Second stage (called adiabatic expansion)

The barrel is removed from the source and is placed over the insulating stand. The piston is pushed back so that the gas expands adiabatically, resulting in a fall of temperature from T₁ to T₂. The conditions of the gas change from B(P₂, V₂) to C(P₃, V₃). If W₂ is the work done in this case, then

W₂ = nCv(T₂ – T₁)

3. Third stage (called isothermal compression)

The barrel is placed over the sink. The piston is pushed down, thereby compressing the gas. The heat generated due to compression flows to the sink, maintaining the temperature of the barrel constant. The state of the gas changes from  C(P₃, V₃) to D(P₄, V₄). If W is the work done in this process and Q is the heat rejected to the sink, then

W₃ = -nRT₂ loge(V₄ / V₃)

4. Fourth stage (called adiabatic compression) 

The barrel is placed over the insulating stand. The piston is moved down, thereby compressing the gas adiabatically till the temperature of gas increases from T₂ to T₁. The state of gas changes from D(P₄, V₄) to   A(P₁, V₁). If W₄ is the work done in this process, then

W₄ =  nCv(T₁ – T₂)

Answer 2

Explanation isothermal expansion (curve AB)

Explanation adiabatic expansion (curve BC)

Explanation isothermal compression (curve CD)

Explanation adiabatic compression (curve DA)

Detailed Answer :

Carnot cycle : A carnot engine consists of

(i) A source of heat at temperature T₁

(ii) A sink at temperature T₂ such that T₁ > T₂.

(iii) A cylinder with conducting base with ideal gas as a working substance.

(iv) In insulating stand,

As the engine works, the working substance of the engine undergoes a cycle known as Carnot cycle.

(i) First Step : Isothermal expansion curve AB. The cylinder with gas is allowed to expand slowly at constant

temperature T₁ by putting in on the source.

Work done = heat absorbed by the system.

(ii) Second Step : Adiabatic expansion the cylinder is kept on the insulating stand while still expanding the gas (adiabatic) till the temperature falls to 7.

(iii) Third Step : Isothermal compression, the cylinder is placed on the sink and the gas is compressed at constant temperature T₂