Work done and Heat Transferred

Applying the first law of thermodynamics to the process

dU = dQ - dW

Replacing dW with the reversible work

dU = dQ - PdV

The volume will change as the gas is heated at constant pressure. To make calculations more straight forward, use ENTHALPY, H

H = U + PV

dH = dU + PdV + VdP

rearrange for dU

dU = dH - PdV - VdP

and substitute into the first law

dH - PdV - VdP = dQ - PdV

the PdV terms cancel out and since pressure is constant dP = 0, so that

dH = dQ

The definition of the specific heat at constant pressure

is used to replace dH in the first law

During a constant pressure process, heat is added or removed and the temperature and volume change. The volume at the end of the process can be found using the ideal gas law and the work calculated from

Entropy Change

Starting with the first law expression for the process

dH = dQ

and replacing dH from the definition of specific heat at constant pressure and Dq from the definition of entropy