**Isothermal Expansion of Carnot Cycle:**

Let consider one mole of an ideal gas enclosed in the cylinder. Let V_{1}, P_{1} be the initial volume and pressure of the gas respectively. The initial state of the gas is represented by the point A on the P-V diagram. The cylinder is placed over the source which is at the temperature T_{1}.

The piston is allowed to move slowly outwards, so that the gas expands. Heat is gained from the source and the process is isothermal at constant temperature T_{1}. In this process the volume of the gas changes from V_{1} to ; and the pressure changes from P_{1} to P_{2}. This process is represented by AB in the indicator diagram (Figure).

During this process, the quantity of heat absorbed from the source is Q_{1} and W_{1} is the corresponding amount of work done by the gas.

**Q _{1} = W_{1} = ^{v2}∫_{v1} PdV =RT_{1} log_{e} (V_{2}/V_{1})**

**= Area ABGEA**