Question

show that foran ideal gas dw is not an exact differential
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Answer 1

Answer:

Show that for an ideal gas, the work differential dw is not an exact differential. But it brings contradiction as there is always a change in volume with temperature at constant pressure. This leads to the conclusion that dw is not an exact differential.

Answer 2

Show that for an ideal gas dw is not an exact differential:

Explanation:

• dw= PdV …..1
• Volume V is a state function i.e. it is independent of the path [V=f (T,P)] hence dV is an exact differential.
• dv =(∂v/∂T)_p dT + (∂v/∂P)_T dP
• For an ideal gas, we know that PV = RT which means:
• V= RT/P
• dw = PdV = RdT – (RT/P) dP = RdT – VdP
• (∂V/∂T) P = 0
• But it brings contradiction as there is always a change in volume with temperature at constant pressure. This leads to the conclusion that dw is not an exact differential.