Classes

distler Administator 20 posts

Here is a table summarizing how various thermodynamic quantities change, when an ideal gas undergoes various processes.

Process	$p$ - $V$ curve	$Δ U$	$Q$	$W$	$Δ S$
isothermal ( $T = const$ )	$p V = const$	$0$	$N k T \ln (V_{f} / V_{i})$	$N k T \ln (V_{f} / V_{i})$	$N k \ln (V_{f} / V_{i})$
adiabatic ( $Q = 0$ )	$p V^{γ} = const$	$α N k (T_{f} - T_{i})$	$0$	$- α N k (T_{f} - T_{i})$	$0$
iso-volume ( $V = const$ )	$V = const$	$α N k (T_{f} - T_{i})$	$α N k (T_{f} - T_{i})$	$0$	$α N k \ln (T_{f} / T_{i})$
isobaric ( $p = const$ )	$p = const$	$α N k (T_{f} - T_{i})$	$(α + 1) N k (T_{f} - T_{i})$	$N k (T_{f} - T_{i})$	$(α + 1) N k \ln (T_{f} / T_{i})$

The basic equations are

\begin{aligned} Ideal Gas Law: & p V & = N k T = \frac{1}{α} U \\ First Law: & Δ U & = Q - W \\ Entropy: & Q & = T Δ S \\ Work: & W & = p Δ V \end{aligned}

Here

α = {\begin{array}{ll} \frac{3}{2} & monatomic gase \\ \frac{5}{2} & diatomic gase \end{array}

is related to the molar specific heat at constant volume

c_{V} = α R

and $γ = \frac{(α + 1)}{α}$ is the ratio of specific heats

γ = c_{p} / c_{V}

Ideal Gas Changes of State