• id: JTHERM-01-N08
• title: Constant Pressure and Constant Volume Processes
• tags: isobaric, isochoric, Cv, Cp

Isobaric (P = constant): $W = P\Delta V = nR\Delta T$. $Q = nC_p\Delta T$. $\Delta U = nC_v\Delta T$. Verification: $Q = \Delta U + W \Rightarrow nC_p\Delta T = nC_v\Delta T + nR\Delta T \Rightarrow C_p = C_v + R$ (Mayer's relation). On P-V diagram: horizontal line.

Isochoric (V = constant): $W = 0$. $Q = \Delta U = nC_v\Delta T$. All heat goes to internal energy. On P-V diagram: vertical line. Heating in a rigid container is isochoric. Gay-Lussac's law: $P/T = \text{constant}$.