Two identical balls, $A$ and $B$ , of uniform composition and initially at the same temperature, each absorb exactly the same amount of heat. $A$ is hanging down from the ceiling while $B$ rests on the horizontal floor in the same room. Assuming no subsequent heat loss by the balls, which of the following statements is correct about their final temperatures, $T_A$ and $T_B$ , once the balls have reached their final state?

In the reported figure, there is a cyclic process $ABCDA$ on a sample of $1\, {mol}$ of a diatomic gas. The temperature of the gas during the process ${A} \rightarrow {B}$ and ${C} \rightarrow {D}$ are ${T}_{1}$ and ${T}_{2}\left({T}_{1}\,>\,{T}_{2}\right)$ respectively.

Choose the correct option out of the following for work done if processes $B C$ and $D A$ are adiabatic.

A hypothetical gas expands adiabatically such that its volume changes from $8$ litres to $27$ litres. If the ratio of final pressure of the gas to initial pressure of the gas is $\frac{16}{81}$. Then the ratio of $\frac{C_P}{C_V}$ will be

A certain amount of gas is taken through a cyclic process $(A\,B\,C\,D\,A)$  that has two isobars, one isochore and one isothermal. The cycle can be represented on a $P-V$ indicator diagram as

Two samples $A$ and $B$ of a gas initially at the same pressure and temperature are compressed from volume $ V$ to $ V/2$ ($A$ isothermally and adiabatically). The final pressure of $ A$ is