Question

Starting out on a trip to the mountains, you inflate the tires on your automobile to a recommended pressure of $3.9\times {10}^5\text{Pa}$ on a day when the temperature is $-{13.0}^{\circ }\text{C}$. You drive to the beach, where the temperature is ${36.0}^{\circ }\text{C}$. Assume that the volume of the tire has increased by $3\%$. What is the final pressure of air in the tires?

• A. $4.50\times {10}^5\text{Pa}$
• B. $4.65\times {10}^5\text{Pa}$
• C. $3.50\times {10}^5\text{Pa}$
• D. $11.1\times {10}^5\text{Pa}$

Answer 1

The correct option is A $4.50\times {10}^5\text{Pa}$

Assuming no loss of air, ${}^{\prime }{n}^{\prime }$ remains constant.
$\therefore \frac{P_1{V}_1}{R{T}_1}=\frac{P_2{V}_2}{R{T}_2}$. [Here, $V_2=1.03V_1$
$\therefore P_2=P_1\times \frac{V_1}{V_2}\times \frac{T_2}{T_1}=3.9\times {10}^5\times \frac{V_1}{1.03V_1}\times \frac{309K}{260K}$
$=4.5\times {10}^5\text{Pa}$