$A$ gas is compressed at constant temperature. Its molecules gain:

Can the temperature of a system remain constant even when it is heated? Explain.

$A$ vertical cylinder with heat-conducting walls is closed at the bottom and is fitted with a smooth light piston. It contains one mole of an ideal gas. The temperature of the gas is always equal to the surrounding's temperature,$T_0$. The piston is moved up slowly to increase the volume of the gas to $\eta$ times. Which of the following is incorrect?

One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature,$27\,^{\circ}C$. The work done on the gas will be

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 ...... $J$. $(R = 8.31 \, J/mol \cdot K)$

An ideal gas is trapped inside a test tube of cross-sectional area $20 \times 10^{-6} \, m^2$ as shown in the figure. The gas occupies a height $L_1$ at the bottom of the tube and is separated from air at atmospheric pressure by a mercury column of mass $0.002 \, kg$. If the tube is quickly turned isothermally,upside down,the gas now occupies height $L_2$ in the tube. Find the ratio $L_2/L_1$. [Take atmospheric pressure $P_0 = 10^5 \, Nm^{-2}$ and $g = 10 \, ms^{-2}$]