Kinetic Theory Of Gases Question 70
Question: Air is pumped into an automobile tube up to 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
Options:
A) 212 kPa
B) 209 kPa
C) 206 kPa
D) 200 kPa
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ \frac{P _{1}V _{1}}{T _{1}}=\frac{P _{2}V _{2}}{T _{2}} $ Here, $ P _{1}=200kPa $
$ T _{1}=22{}^\circ C=295K~~~~~~T _{2}=42{}^\circ C=315K $
$ V _{2}=V _{1}+\frac{2}{100}V _{1}=1.02V _{1} $
$ \
Therefore ,P _{2}=\frac{200\times 315V _{1}}{295\times 1.02V _{1}}=209.97kPa $
BETA
