An ideal gas is initially at temperature $T$ and volume $V.$ Its volume is increased by $\Delta V$ due to an increase in temperature $\Delta T,$ pressure remaining constant. The quantity $\delta = \Delta V / (V \Delta T)$ varies with temperature as

Inside a cylinder having insulating walls and closed at ends is a movable piston,which divides the cylinder into two compartments. On one side of the piston is a mass $m$ of a gas and on the other side a mass $2m$ of the same gas. What fraction of the total volume of the cylinder will be occupied by the larger mass of the gas when the piston is in equilibrium? Consider that the movable piston is conducting so that the temperature is the same throughout.

Two spherical vessels of equal volume $V$ are connected by a narrow tube. The apparatus contains an ideal gas at $1 \text{ atm}$ and $300 \text{ K}$. Now,if one vessel is immersed in a bath of constant temperature $600 \text{ K}$ and the other in a bath of constant temperature $300 \text{ K}$,then the common pressure will be ...... $\text{atm}$.

An ideal gas undergoes a process maintaining the relation between pressure $(P)$ and volume $(V)$ as $P = P_o(1 + (\frac{V_o}{V})^2)^{-1}$, where $P_o$ and $V_o$ are constants. If two samples $A$ and $B$ (two moles each) with initial volumes $V_o$ and $3V_o$ respectively undergo the above-mentioned process, calculate the difference in the temperatures of these samples, $T_B - T_A$, assuming the process is evaluated at their initial states. ($R$ = gas constant)

The temperature of an open room of volume $30\ m^3$ increases from $17^\circ C$ to $27^\circ C$ due to sunshine. The atmospheric pressure in the room remains $1 \times 10^5\ Pa$. If $n_i$ and $n_f$ are the number of molecules in the room before and after heating,then $n_f - n_i$ will be:

The pressure versus temperature graph of an ideal gas with an equal number of moles at different volumes is plotted as shown in the figure. Choose the correct alternative.