First slide

Thermodynamic processes

Question

The pressure in the tyre of a car is four times the atmospheric pressure at 300 K. If this tyre suddenly bursts, its new temperature will be $(γ = 1 .4)$

Moderate

A

$300 {(4)}^{1 .4 / 0 .4}$
B

$300 {(\frac{1}{4})}^{- 0.4 / 1.4}$
C

$300 {(2)}^{- 0.4 / 1.4}$
D

$300 {(4)}^{- 0.4 / 1.4}$

Solution

For adiabatic process $\frac{T^{γ}}{P^{γ - 1}} =$ constant
$\Rightarrow \frac{T_{2}}{T_{1}} = {(\frac{P_{1}}{P_{2}})}^{\frac{1 - γ}{γ}} \Rightarrow \frac{T_{2}}{300} = {(\frac{4}{1})}^{\frac{(1 - 1 .4)}{1 .4}} \Rightarrow T_{2} = 300 (4)^{- \frac{0 .4}{1 .4}}$

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