An ideal gas at temperature $T$, pressure $p$ occupies a volume $V$. If its temperature is halved and pressure doubled, what is its new volume?

A Carnot engine whose efficiency is $40 \%$, receives heat at 500 K . If the efficiency is to be $50 \%$, the source temperature for the same exhaust temperature is

A system goes from $A$ and $B$ via two processes I and II as shown in figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes I and II respectively, then the relation between $\Delta U_1$ and $\Delta U_2$ is

An organ pipe with both ends open has a length $L=25$ cm . An extra hole is created at position $L / 2$. The lowest frequency of sound produced is (assume, speed of sound $=340 \mathrm{~m} / \mathrm{s}$ )