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 -  1.5

B -   1.67

C-  1.4

D -  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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