A car tyre has a volume of 10 litres when inflated. The tyre is inflated to a pressure of 3 atm at $17^{0} C$ with air. Due to driving the temperature of tyre increases to $47^{0} C$ .

(a) What would be the pressure at this temperature?
(b) How many litres of air measured at $47^{0} C$ and pressure of 1 atm should be let out to restore the tyre to 3 atm at $47^{0} C$ ?

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Solution

Given
$(a) P_{1} = 3 a t m$
$T_{1} = 17^{o} C = 290 k$
$V_{1} = 10 C$
$P_{2} = ?$
$T_{2} = 47^{o} C = 320 k$

for a constant volume
$\frac{P_{1}}{P_{2}} = \frac{T_{1}}{T_{2}}$

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

$\frac{3 \times 320}{290} = 3.31 a t m$

$(b)$ pressure to be restored $= 3 a t m$
decrease in pressure $= 3.31 - 3$
$= 0.31 a t m$

Let $V$ be the volume that is let out
$∴$ at constant temperature
$P_{1} V_{1} = P_{2} V_{2}$
$0.31 \times 10 = 1 \times V$
$V = 3.1 L$

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