Question

Air is pumped into an automobile tyre's tube up to a pressure of 200 kPa in the morning when the air temperature is 20°C. During the day the temperature rises to 40°C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature.

Answer 1

$\begin{array}{l}\text{Here,}\\ P_1=2\times {10}^5\mathrm{Pa}\\ P_2=?\\ T_1=293K\\ T_2=313K\\ V_2=V_1+0.02V_1=V_1\left(1.02\right)\\ \text{Now,}\\ \frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\\ \Rightarrow \frac{2\times {10}^5{V}_1}{293}=\frac{P_2{V}_1\left(1.02\right)}{313}\\ \Rightarrow P_2=\frac{2\times {10}^5\times 313}{293\times 1.02}=209\text{kPa}\end{array}$