Isothermal Compression of Carnot Cycle

Isothermal compression of Carnot Cycle

The cylinder is placed on the sink at a temperature T₂. The piston is moved slowly downward to compress the gas isothermally. This is represented by CD. Let (V₄, P₄) be the volume and pressure corresponding to the point D. Since the base of the cylinder is conducting the heat produced during compression will pass to the sink so that, the temperature of the gas remains constant at T₂. Let Q₂ be the amount of heat rejected to the sink and W₃ be the amount of work done on the gas in compressing it isothermally.

Q₂ = W₃ = ^v4∫_v3 – PdV = – RT₂ log_e (V₄/V₃) = – Area CDFHC

The negative sign indicates that work is done on the working substances.

So, Q₂ = RT₂ log_e (V₃/V₄)