Question

Air is pumped into an automobile tyre's tube up to a pressure of $200\text{kPa}$ in the morning when the air temperature is ${27}^{\circ }\text{C}$ During the day, the temperature rises to ${47}^{\circ }\text{C}$ and the tube expands by $3$ percent. Calculate the pressure of the air in the tube at this temperature.

• A. $200\text{kPa}$
• B. $207\text{kPa}$
• C. $215\text{kPa}$
• D. $195\text{kPa}$

Answer 1

The correct option is B $207\text{kPa}$

Given that
$P_1=2\times {10}^5\text{Pa}{T}_1=300\text{K}$
Let initial volume $V_1=V$
Final pressure $P_2=??$
$T_2=273+47=320\text{K}$
& $V_2=1.03V$

Number of moles will remain conserved
So, $n_1=n_2$
$\frac{P_1{V}_1}{R{T}_1}=\frac{P_2{V}_2}{R{T}_2}$
$\Rightarrow P_2=\frac{P_1{V}_1{T}_2}{T_1{V}_2}=\frac{2\times {10}^5\times V\times 320}{300\times 1.03\times V}$
$\Rightarrow P_2=2.071\times {10}^5\text{Pa}$
$\Rightarrow P_2\approx 207\text{kPa}$