Is the volume expanded and the volume compressed during carnot cycle is equal?

Answer 1

Since it is a CYCLE, the overall volume change from minimum volume to maximum volume and back must sum to zero, thus the volume expanded must equal the volume compressed. Now, bear in mind that the Carnot Cycle consists of 4 steps:

1. Reversible isothermal expansion of the gas at the "hot" temperature, T1 (isothermal heat addition or absorption).
2. Isentropic (reversible adiabatic) expansion of the gas (isentropic work output).
3. Reversible isothermal compression of the gas at the "cold" temperature, T2. (isothermal heat rejection)
4. Isentropic compression of the gas (isentropic work input).

Although when you graph the cycle on a PV diagram, it looks pretty similar, there is no requirement that the volume change in step 1 matches the volume change in step 3, nor that the volume change in step 2 match that in step 4.