Question

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.

Answer 1

The pressure of the air in the tube at this temperature is $P_{2}=209 \mathrm{kpa}$

Explanation:

Step 1:  

Given data,  

$P_{1}=2 \times 10^{5} \mathrm{Pa}$

$P_{2}=?$

$T_{1}=293 \mathrm{K}$

$T_{2}=313 \mathrm{K}$

Step 2:

$\mathrm{V}_{2}=\mathrm{V}_{1}+\mathrm{O} . \mathrm{O} 2 \mathrm{V}_{1}$

$=V_{1}(1+0.02)$

$=1.02 \mathrm{V}_{1}$

Step 3:

we know that  

$\frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}}$

$\frac{2 \times 10^{5} V_{1}}{293}=\frac{1.02 V_{1} P_{2}}{313}$

$\frac{2 \times 10^{5}}{293}=\frac{1.02 P_{2}}{313}$

$P_{2}=\frac{2 \times 10^{5} \times 313}{293 \times 1.02}$

$P_{2}=\frac{626 \times 10^{5}}{298.86}$

$P_{2}=2.09 \times 10^{5}$

$P_{2}=209 \times 10^{3} \mathrm{pa}$

$P_{2}=209 \mathrm{kpa}$