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?

If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamical process, which of the following is true?

If $\gamma = 2.5$ and volume is equal to $\frac{1}{8}$ times to the initial volume then pressure $P' $ is equal to (Initial pressure $= P$)

Graph $A-B$ is an adiabatic curve. Choose the correct statement

A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure. Find heat exchanged by the engine, with the surroundings for each section of the cycle.${C_v} = \frac{3}{2}R$

$(a)$ $A$ to $B$ : constant volume

$(b)$ $B$ to $C$ : constant pressure

$(c)$ $C$ to $D$ : adiabatic

$(d)$ $D$ to $A$ : constant pressure