Question

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

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

Answer 1

The correct option is B $209kPa$

$\begin{array}{c}Given{P}_1=200kpa\\ T_1={22}^{\circ }C=273+22-295K\\ T_2={42}^{\circ }C=273+42=315K\\ PV=nRT\\ \left(\frac{PV}{T}\right)=constant\left[\begin{array}{c}Sincenumberofmoles\\ andRareconstant\end{array}\right]\\ \frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\\ \frac{200\times 1}{295}=\frac{P_2\left(1.02\right)}{315}\\ P_2=\frac{200\times 315}{295\times 1.02}kPa\\ =209kPa\end{array}$

Option B.