Question

For the same expansion ratio work done by a gas in case of adiabatic processes as compared to isothermal process is

Answer 1

Answer:

The sign simply tells us whether the system (say ideal gas) is performing work on the surroundings (positive work, where energy is transferred out of the system), or the surroundings are performing work on the system (negative work, where energy is transferred into the system). In each case, the amount of work equals the magnitude of the energy transferred, regardless of whether it is positive or negative. In all cases the transfers are governed by the first law: ΔU=Q−W.

If we include the sign then work done in adiabatic expansion as well as contraction is greater than the work done in isothermal process

From the graphs provided by @drew, if the system starts at the same equilibrium state and expands to the same final volume, you can clearly see that the positive isothermal work is greater than the positive adiabatic work since the area under the pV curve is greater. The reason is the isothermal expansion process uses the heat transferred from the surroundings to do its work, whereas for the adiabatic expansion Q=0 and the process uses the system’s internal energy to perform its work. This results in a greater drop in pressure for the adiabatic expansion to reach the final volume than that for the isothermal expansion, and thus less area under the pV curve and less work.

When the processes are reversed, the pressure rises at a faster rate for the adiabatic process (because all of the energy of the work done on the system increases its internal energy) than the isothermal process (because all of the energy of the work done on the system transfers out as heat). As a result, more negative work has to be done by the isothermal process to return to the same initial pressure as the adiabatic process. The adiabatic work may be less negative, but as previously stated, the amount of work depends only on its magnitude.