Question

In an isothermal process on an ideal gas, the pressure increases by 0.5%. The volume decreases by about
(a) 0.25%
(b) 0.5%
(c) 0.7%
(d) 1%.

Answer 1

(b) 0.5%

Let p and p' be the initial and final pressures of the system and V and V' be the initial and final volumes of the system. p' is 0.5% more than p and the process is isothernal. So, pV = k = p'V' = constant. Therefore,
$$\begin{gathered} pV=p\text{'}V\text{'} \\ \Rightarrow pV=\left(p+\frac{0.5}{100}p\right)V \\ \Rightarrow pV=\frac{100.5}{100}pV\text{'} \\ \Rightarrow V\text{'}=\frac{100}{100.5}V \\ \Rightarrow V\text{'}-V=\frac{100}{100.5}V-V \\ =-\frac{0.5}{100.5} \\ =-0.49\% \end{gathered}$$
So, volume V' decreases by about 0.5% of V.