First slide

Different type of processes

Question

A mass of diatomic gas ( $γ = 1.4$ ) at a pressure of 2 atm is compressed adiabatically so that its temperature rise from $27^{0} C to 927^{0} C .$ The pressure of the gas is final state is

Moderate

A

28 atm
B

68.7 atm
C

256 atm
D

8 atm

Solution

$T_{1} = 273 + 27 = 300 K$
$T_{2} = 273 + 927 = 1200 K$
Gas equation for adiabatic process ${pV}^{γ} = constant$
$p {(\frac{T}{p})}^{γ} = constant (∴ pV = RT)$
$\frac{p_{2}}{p_{1}} = {(\frac{T_{2}}{T_{1}})}^{\frac{γ}{γ - 1}} or p_{2} = p_{1} {(\frac{T_{2}}{T_{1}})}^{\frac{γ}{γ - 1}}$
$p_{2} = 2 {(\frac{1200}{300})}^{\frac{1.4}{1.4 - 1}}$
$p_{2} = 256 atm .$

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