Cooking gas containers are kept in a lorry moving with uniform speed. The temperature of the gas molecules inside will

During an experiment,an ideal gas is found to obey a condition $\frac{P^2}{\rho} = \text{constant}$ [$\rho = \text{density of the gas}$]. The gas is initially at temperature $T$,pressure $P$,and density $\rho$. The gas expands such that density changes to $\rho/2$.

$A$ gas is filled in the cylinder shown in the figure. The two pistons are joined by a string. If the gas is heated,the pistons will

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the Statements,choose the one that best describes the two Statements.
Statement-$1$: The internal energy of a perfect gas is entirely kinetic and depends only on the absolute temperature of the gas and not on its pressure or volume.
Statement-$2$: $A$ perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat,the temperature rise of the gas at constant pressure is lower than that at constant volume.

When the gas is heated,in which direction will the piston move?

$A$ gas has temperature $T$ and volume $V$. At constant pressure,if the temperature is increased by $\Delta T$,the volume increases by $\Delta V$. How does $\delta = \frac{\Delta V}{V\Delta T}$ vary with temperature?