Is heat δ Q an exact differential for an isochoric process (ideal gases)?

Question

Is heat   δ  Q an exact differential for an isochoric process (ideal gases)?

Melany Flynn · Accepted Answer

Let&#039;s assume that the system is in equilibrium throughout the isochoric process and closed. We say the process has to be quasi-static. Under these conditions the work done on the system is  δ  W  =  −  p  d  V  +      ∑    i        y    i        X    i  where the       X    i   represent different work variables, arising from different physical interactions. For example the work on a closed homogenous system done by electrical or magnetic field is  δ  W  =  −  p  d  V  +            E      →        d            P      →        +            H      →        d            M      →      Let&#039;s assume the only work coordinate in question is the volume V due to compression of the system. And let&#039;s furthermore assume that we only move in the thermodynamic subspace spanned by V=const. Then we indeed have  δ  W  =  0And by the first law of thermodynamics  d  U  =  δ  QAs the LHS is integrable the RHS has to be as well. So the state function Q exists for systems undergoing quasi static processes on the subspace defined by V=const. under the ssumptions that no other work coordinates are involved. But I don&#039;t see any reason how this would be useful.

Is heat δQ an exact differential for an isochoric process (ideal gases)?

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