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

Question

Air is pumped into an automobile tube upto a pressure of 200 kPa in the morning when the air temperature is 22°C. During the day, temperature rises to 42°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

Tardigrade Admin · Accepted Answer

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

∴ \frac{p _{1} V _{1}}{T _{1}} = \frac{p _{2} V _{2}}{T _{2}}

Given

P_{1} = 200 k p a, V_{1}, = T_{1} = 273 + 22 = 295 K,

V_{2} = V + 0.02 V, T_{2} = 273 + 42 = 315 K

\frac{200 \times V}{295} = \frac{p _{2} \times 1.02 V}{315}

\Rightarrow p_{2} = \frac{200 \times 315}{295 \times 1.02}

p_{2} \approx 209 k P a

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

212 kPa

209 kPa

206 kPa

200 kPa

Q. 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