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 200${}^{\circ }$C. During the day the temperature rises to 400${}^{\circ }$C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature

• A. 209 kPa
• B. 285 kPa
• C. 355 kPa
• D. 392 kPa

Answer 1

The correct option is D

392 kPa

The ideal gas equation relates the state variables as: PV = nRT. Assuming no leakage in the tyre, it is safe to assume that the number of moles of air, n, has not changed in the process. Thus, the fraction $n=\left(\frac{pv}{RT}\right)$ will be constant.

Also, if the initial volume is V, the final volume will be $[\frac{102}{100}\times V],or1.02V.$

Denoting the final pressure as $P_f$, we can write -

$n=\left[\frac{P_f\times 1.02V}{R\times 40}\right]=\left[\frac{200\times V}{R\times 20}\right]$

$\Rightarrow P_f=\left(\frac{200\times 40}{20\times 1.02}\right)kPa=392kPa.$