The pressure and density of a diatomic gas - - 7-5 change adiabatically form p1- d1 to p2- d2- If d2-d1-32- then p2-p1 is

_pV^γ = constant. For a given mass of gas, V ∝1/d. Hence p/d^γ= constant ∴p_1/d_1^γ = p_2/d_2^γ or p_2/p_1 = ( d_2/d_1 )^γ = (32)^7/5 = (2)^7 = 128 ...

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Byju's Answer

Standard XII

Physics

Heat Capacity

The pressure ...

Question

The pressure and density of a diatomic gas $(γ = \frac{7}{5})$ change adiabatically form $(p_{1}, d_{1})$ to $(p_{2}, d_{2})$ . If $\frac{d_{2}}{d_{1}} = 32, t h e n \frac{p_{2}}{p_{1}}$ is

$\frac{1}{128}$

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128

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256

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Solution

The correct option is C
128

$_{p} V^{γ} = c o n s t a n t$ . For a given mass of gas, $V \propto \frac{1}{d}$ .
Hence
$\frac{p}{d^{γ}} = c o n s t a n t ∴ \frac{p_{1}}{d_{1}^{γ}} = \frac{p_{2}}{d_{2}^{γ}} o r \frac{p_{2}}{p_{1}} = {(\frac{d_{2}}{d_{1}})}^{γ} = (32)^{\frac{7}{5}} = (2)^{7} = 128$

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The pressure and density of a diatomic gas $(γ = \frac{7}{5})$ change adiabatically form $(p_{1}, d_{1})$ to $(p_{2}, d_{2})$ . If $\frac{d_{2}}{d_{1}} = 32, t h e n \frac{p_{2}}{p_{1}}$ is