Qstnid -Iv-23-air Is Pumped Into An Automobile Tyre’s Tube Up To A Pressure Of 200 Kpa In The Morning When The Air Temperature Is 20°c. During The Day The Temperature Rises To 40°c And The Tube Expands By 2%. Calculate The Pressure Of The Air In The Tube At This Temperature. - 24: Kinetic Theory Of Gases

with Solutions - page 5

#23
Air is pumped into an automobile tyre’s tube up to a pressure of 200 kPa in the morning when the air temperature is 20°C. During the day the temperature rises to 40°C and the tube expands by 2%. Calculate the pressure of the air in the tube at this temperature.
Ans : `` \begin{array}{l}\text{Here,}\\ {P}_{1}=2\times {10}^{5}\,\mathrm{\,Pa\,}\\ {P}_{2}=?\\ {T}_{1}=293K\\ {T}_{2}=313K\\ {V}_{2}={V}_{1}+0.02{V}_{1}={V}_{1}\left(1.02\right)\\ \text{Now,}\\ \frac{{P}_{1}{V}_{1}}{{T}_{1}}=\frac{{P}_{2}{V}_{2}}{{T}_{2}}\\ \Rightarrow \frac{2\times {10}^{5}{V}_{1}}{293}=\frac{{P}_{2}{V}_{1}\left(1.02\right)}{313}\\ \Rightarrow {P}_{2}=\frac{2\times {10}^{5}\times 313}{293\times 1.02}=209\text{kPa}\end{array}``
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