# A monoatomic gas is going under adiabatic process. adiabatic elasticity at pressure $\mathrm{P}=10^{3} \mathrm{~N} / \mathrm{m}^{2} \ is \ \mathrm{K} \ times \ 10^{3} \mathrm{~N} / \mathrm{m}^{2} \ \ then \ \ value \ \ of \ \mathrm{K} \ \ is$A -  1.5B -   1.67C-  1.4D -  1.3

Answers (1)

For adiabatic process $PV^\gamma = constant \: \: di\! f\! \! f\! erentiating \: \: both \: \: side$

$dPV^\gamma + P_\gamma V^{\gamma -1}dV = 0$

$\gamma P = \frac{dP}{-dv/v} = \frac{stress }{strain } = elasticity \\\\ adiabatic \: \: elasticity = \gamma P \\\\ = 5/3 \times 10 ^3 \\\\ = 1.67 \times 10 ^ 3$

For adiabatic process $PV^\gamma = constant \: \: di\! f\! \! f\! erentiating \: \: both \: \: side$

$dPV^\gamma + P_\gamma V^{\gamma -1}dV = 0$

$\gamma P = \frac{dP}{-dv/v} = \frac{stress }{strain } = elasticity \\\\ adiabatic \: \: elasticity = \gamma P \\\\ = 5/3 \times 10 ^3 \\\\ = 1.67 \times 10 ^ 3$

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