COMEDK2022ChemistryThermodynamics (C)
The difference between heat capacity at constant pressure and heat capacity at constant volume is
Options
- AR
- BR T
- CR V
- D1
Correct answer
A. R
Step-by-step solution
For an ideal gas, the enthalpy H is defined as H = U + PV . Differentiating with respect to temperature T at constant pressure, we have ( H T )_P = ( U T )_P + P ( V T )_P . By definition, C_P = ( H T )_P and C_V = ( U T )_V . For an ideal gas, U depends only on temperature, so ( U T )_P = ( U T )_V = C_V . Using the ideal gas equation PV = nRT , for one mole ( n=1 ), PV = RT . Differentiating with respect to T at constant pressure gives P ( V T )_P = R . Substituting these into the enthalpy derivative equation, we