Heat Loss or Gain During a Change of State for a Gas

The heat received by the gas during a process which changes the state of the gas is  
\[\oint_C dU + p dV\]
  is a function of  
. We can define the state of a gas using these two coordinates, so a point  
  is a closed curve  
\[\oint_C dU =0\]
  and the gas gains heat energy equal to  
\[\oint_C p dV\]

This is the area enclosed by the curve  

If the curve  
  is described clockwise then the area is taken as positive and the gas experiences a net gain of heat energy.

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