Question

Air is pumped into an automobile tube up to a pressure of $200 \, kPa$ in the morning when the air temperature is $22 \, ℃$ . During the day, the temperature rises to $42 \, ℃$ and the tube expands by $2\%$ . The pressure of the air in the tube at this temperature will be approximately

• A. $212\,kPa$
• B. $209\,kPa$
• C. $206\,kPa$
• D. $200\,kPa$

Answer 1

Answer: (B)

The ideal gas law is the equation of state of an ideal gas. The state of an amount of gas is determined by its pressure, volume and temperature. The equation has the form
$pV=nRT$
where, $p$ is pressure, $V$ the volume, $n$ the number of moles, $R$ the gas constant and $T$ the temperature.
$\therefore \, \, \, \frac{p_{1} V_{1}}{T_{1}}=\frac{p_{2} V_{2}}{T_{2}}$
Given, $p_{1}=200 \, kPa, \, V_{1}=V, \, T_{1}=273+22=295 \, K, \, V_{2}=V+0.02 \, V$
$T_{2}=273+42=315$ K
$\frac{200 \times V}{295}=\frac{p_{2} \times 1.02 V}{315}$
$\Rightarrow \, \, p_{2}=\frac{200 \times 315}{295 \times 1.02}$
$p_{2}=209 \, $ $kPa$