$A$ certain gas is isothermally compressed to $(1/3)^{rd}$ of its initial volume $(V_0 = 3 \ \text{L})$ by applying required pressure. If the bulk modulus of the gas is $3 \times 10^5 \ \text{N/m}^2$, the magnitude of work done on the gas is . . . . . . $J$.

$A$ perfect gas of volume $5 \ L$ is compressed isothermally to a volume of $1 \ L$. The $r.m.s.$ speed of the molecules will

For an ideal gas, in an isothermal process:

One mole of an ideal gas expands at a constant temperature of $300 \, K$ from an initial volume of $10 \, L$ to a final volume of $20 \, L$. The work done in expanding the gas is ...... $J$. $(R = 8.31 \, J/mol \cdot K)$

The work done to increase the volume of $2$ moles of an ideal gas from $V$ to $2V$ at a constant temperature $T$ is $W$. The work to be done to increase the volume of $2$ moles of the same gas from $2V$ to $4V$ at the same constant temperature $T$ is:

Two identical containers $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The mass of the gas in $A$ is ${m_A}$ and that in $B$ is ${m_B}$. The gas in each cylinder is now allowed to expand isothermally to the same final volume $2V$. The changes in the pressure in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$ respectively. Then: