Can All Heat Be Converted to Work in Isothermal Expansion?

[Ritz_physics]

It is understood that energy supplied in the form of work can be completely converted to heat.
However energy transferred in the form of heat cannot be completely obtained from the system as work.

But, consider this case: A Q amount of heat is supplied isothermally to a gas confined in a piston-cylinder device. By the energy balance equation:
ΔU = Q - W
Since ΔU = Cv.ΔT (Cv= specific heat at constant volume, ΔT=0), ΔU = 0.
Hence we get Q= W. This means all of the heat supplied to the gas was obtained as work output from the gas during its isothermal expansion. This comes as a contradiction to the fact that heat cannot be completely converted to work.
Please clarify the doubt.

 

[Infinitum]

Your reasoning is applicable only to ideal gases, which actually do not exist in nature.

 

[Ritz_physics]

Your reasoning is applicable only to ideal gases, which actually do not exist in nature.

But reversible processes also do not exist in nature, even then Kelvin-Planck statement of the second law is applicable to reversible cycles.

 

[salzrah]

The way you wrote those equations and presented those equations doesn't prove that you have showed a way that heat can be turned into work.
All you really wrote was that if the change in potential energy is 0, then the change in heat is equal to the change in work -- according to the equation.
However, an exception was created to that equation which is now called the second law of thermodynamics. This law, in essence, states that heat cannot be changed completely into work, based on the principles of entropy.