Question

One mole of an ideal gas is put through a series of changes as shown in the graph in which $A,B$ and $C$ mark the three stages of the system. At each stage the variables are shown in the graph.
(a) Calculate the pressure at three stages of the system.
(b) Name the process during the following changes:
(i) $A$ to $B$ (ii) $B$to $C$ (iii) $C$ to $A$ (iv) overall change.

Answer 1

(a) Stage $A$:
$V=24.0L;T=300K;n=1;R=0.0821litre-atm$ $K^{-1}{mol}^{-1}$
Substituting these values in the ideal gas equation
$PV=nRT$
$P=\frac{1\times 0.0821\times 300}{23.0}=1.026atm$
(b) At stage $B$
Volume remains the same but temperature changes from $300K$ to $600K$. Thus, according to pressure law, the pressure will be doubled at $B$ with respect to $A$.
Pressure at $B=2\times 1.026=2.052atm$
At stage $C$
Temperature is $300K$ and volume is half that of stage $A$. Thus, according to Boyle's law, the pressure at $C$ will be doubled with respect to $A$
Pressure at $C=2\times 1.026=2.052atm$
(b) (i) During the change from $A$ to $B$, volume remains constant, the process is isochoric.
(ii)During the change from $B$ to $C$, pressure remains constant, the process is isobaric.
(iii) During the change from $C$ to $A$, temperature remains constant, the process is isothermal.
(iv) Overall, the process is cyclic as it returns to initial state.