Question

Air is pumped into an automobile tube upto a pressure of 200 kPa 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. 212 kPa
• B. 209 kPa
• C. 206 kPa
• D. 200 kPa

Answer 1

Answer: (B)

209 kPa

Answer 2

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
$\therefore \, \, \, \, \, \, \frac{p_1 V_1}{T_1} = \frac{p_2V_2}{T_2}$
Given $\, P_1 = 200 kpa, V_1,= T_1 = 273 + 22 = 295 K,$
$V_2 = V + 0.02V , T_2 = 273 + 42 = 315 K$
$\, \, \, \, \, \, \frac{200 \times V}{295} = \frac{p_2 \times 1.02V}{315}$
$\Rightarrow \, \, \, \, \, \, \, \, \, p_2 = \frac{200 \times 315}{295 \times 1.02}$
$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, p_2 \approx 209 kPa$