Answer
See explanation.
Work Step by Step
(a) The ratio of the initial and final temperature is
$\frac{T_c}{T_a } = \frac{p_cV_c}{p_aV_a}$
$\frac{T_c}{T_a } = \frac{(1.0 \times 10^5 Pa)(0.060 m^3 )}{(3.0 \times 10^5 Pa)(0.020 m^3 )}$
$\frac{T_c}{T_a } = 1$
$T_c = T_a$ the initial temperature is the same as the final temperature.
(b) Heat flow, Q in ab. The work done,W is zero because $\Delta V = 0$ It is an isothermal process so there is no change in internal energy.
$Q =0 $
Heat flow in $bc$
$W = p\Delta V$
$W = (1.0 \times 10^5 Pa) (0.060 m^3 - 0.020 m^3 )$
$W = 4.0 \times 10^3 J$
Since It is an isothermal process so there is no change in internal energy.
$ W = Q =4.0 \times 10^3 J $ Heat flows into the system in process $abc$
(c) If the air expands through path a to c, it is changing the pressure and volume hence the bounded area is the work done.
$W = \frac{1}{2} (3.0 \times 10^5 Pa - 1.0 \times 10^5 Pa) (0.060 m^3 - 0.020 m^3 )$
$W = 8.0 \times 10^3 Pa $
Since It is an isothermal process so there is no change in internal energy. So
$Q = W = 8.0 \times 10^3 Pa $
