- #1
weeksy
- 14
- 0
Just a quick question of something I found in my textbook but can't get how they produced it.
C_p =(∂Q/∂T)_p
that is the definition of heat capacity at a constant pressure p. Q is heat and T is temperature. This equation is fine and I know how to derive it. Now it is the next line which worries me.
C_p=(∂Q/∂T)_p = T(∂S/∂T)_p
where S is the entropy
why this bothers me is that this equation as I understand should only hold for C_V (heat capacity with constant volume)
thats because dQ=TdS for a REVERSE-ABLE ONLY expansion (i.e dQ=0 , dS=0) ie adiabatic all of which occur as V, the volume is held constant for C_V. Hence dU=dQ and dQ(rev)=TdS = dU , which can then be simply substituted into the definition. OK
Sorry for the spiel, but my question is how can this same line of reasoning be true for C_p where dV is not constant and dU is not equal to dQ and expansion isn't reversible?
Thanks
C_p =(∂Q/∂T)_p
that is the definition of heat capacity at a constant pressure p. Q is heat and T is temperature. This equation is fine and I know how to derive it. Now it is the next line which worries me.
C_p=(∂Q/∂T)_p = T(∂S/∂T)_p
where S is the entropy
why this bothers me is that this equation as I understand should only hold for C_V (heat capacity with constant volume)
thats because dQ=TdS for a REVERSE-ABLE ONLY expansion (i.e dQ=0 , dS=0) ie adiabatic all of which occur as V, the volume is held constant for C_V. Hence dU=dQ and dQ(rev)=TdS = dU , which can then be simply substituted into the definition. OK
Sorry for the spiel, but my question is how can this same line of reasoning be true for C_p where dV is not constant and dU is not equal to dQ and expansion isn't reversible?
Thanks