A diatomic gas of molecular weight 30 , g/mol | vedclass

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Question

(A) The kinetic energy of the gas is converted into internal energy when it is suddenly stopped.$KE = \Delta U$$\frac{1}{2} m v^2 = n C_v \Delta T$Giv

Vedclass · Accepted Answer

$\frac{60}{R}$

Vedclass · Answer

(A) The kinetic energy of the gas is converted into internal energy when it is suddenly stopped.$KE = \Delta U$$\frac{1}{2} m v^2 = n C_v \Delta T$Given $m = 30 \, g = 0.03 \, kg$,$v = 100 \, m/s$,and $n = \frac{m}{M} = \frac{30 \, g}{30 \, g/mol} = 1 \, mol$.For a diatomic gas,the molar heat capacity at constant volume is $C_v = \frac{R}{\gamma - 1}$. For diatomic gas,$\gamma = 1.4$,so $C_v = \frac{R}{1.4 - 1} = \frac{R}{0.4} = 2.5R$.Substituting the values:$\frac{1}{2} 	imes (0.03) 	imes (100)^2 = 1 	imes \frac{R}{0.4} 	imes \Delta T$$0.5 	imes 0.03 	imes 10000 = \frac{R}{0.4} 	imes \Delta T$$150 = \frac{R}{0.4} 	imes \Delta T$$\Delta T = \frac{150 	imes 0.4}{R} = \frac{60}{R}$

$A$ diatomic gas of molecular weight $30 \, g/mol$ is filled in a container at $27 \, ^\circ C$. It is moving at a velocity of $100 \, m/s$. If it is suddenly stopped,the rise in temperature of the gas is:

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