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$1$ mole of rigid diatomic gas performs a work of $Q / 5$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{ x R }{8},$ The value of $x$ is $\ldots \ldots \ldots .$ $[ K =$ universal gas constant $]$
The temperature of an ideal gas is increased from $120\, K$ to $480\, K.$ If at $120\, K,$ the root mean square velocity of the gas molecules is $v,$ at $480\, K$ it becomes
A gas is filled in a cylinder, its temperature is increased by $20\%$ on kelvin scale and volume is reduced by $10\%$ . How much percentage of the gas will leak out at constant pressure ...... $\%$
A given mass of a gas is allowed to expand freely until its volume becomes double. If ${C_b}$ and ${C_a}$ are the velocities of sound in this gas before and after expansion respectively, then ${C_a}$ is equal to
A diatomic gas of molecules weight $30\,\, gm/mole$ is filled in a container at $27\,^oC$. It is moving at a velocity $100\,\, m/s$. If it is suddenly stopped, the rise in temperature of gas is :
A closed vessel contains $10 g$ of an ideal gas $X$ at $300 \ K$, which exerts $2$ atm pressure. At the same temperature, $80 g$ of another ideal gas $Y$ is added to it and the pressure becomes $6 atm$. The ratio of root mean square velocities of $X$ and $Y$ at $300 \ K$ is