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) 209 kPa

(B) 206 kPa

(C) 200 kPa

(D) 212 kPa

Answer 1

Correct option: (A) 209 kPa

Explanation:

Given: P1 = 200 kpa

T1 = 22°C = 273 + 22 = 295 K

T2 = 42°C = 273 + 42 = 315 K

V2 = 1.02 V1

As PV = nRT

(PV / T) = constant Hence

{(P1 V1) / T1} = {(P2 V2) / T2}

∴ (T2 / T1) = {(P2V2) / (P1V1)}

∴ (315 / 295) = {P2 / 200} × 1.02

∴ P2 = 209 kPa