When to use Specific heat at constant pressure and volume? I\'m having a problem

Question

When to use Specific heat at constant pressure and volume? I'm having a problem differentiate between these two when solving Thermodynamic problem

Explanation / Answer

Just remember these two equations : dU/dT=cV => U2-U1=cV(T2-T1) => (1) dH/dT=cP => H2-H1=cP(T2-T1) => (2) Everywhere you want to calculate internal energy difference and assuming : a-ideal gas , b-constant specific heat coefficient are allowed you can use relation (1). Also for anthalpy difference you are allowed to use relation (2). And this not depends on wether the process is occuring in a constant pressure or constant volume or not. for example when you've a control mass, the 1st law is : Q-W=U2-U1 , Assume we have ideal O2 gas in a piston-cylinder and we heat the gas and then the piston starts to go up. As you know this is a constant pressure process. For a constant pressure process, according to anthalpy definition , Q=H2-H1=cP(T2-T1) . Put this in the 1st law and you'll get : cP(T2-T1)-W=U2-U1 , And now for the term (U2-U1) you can put : cV(T2-T1) , So : W=(cP-cV)(T2-T1)=R(T2-T1) As you saw its not related to wether the process is occuring in constant volume or not, we've used cV(T2-T1) instead of (U2-U1) because of : a-ideal gas , b-constant specific heat coefficient assumptions.

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