If a cylinder containing a gas at high pressure explodes, the gas undergoes

The pressure and density of a diatomic gas $(\gamma = 7/5)$ change adiabatically from $(P, d)$ to $(P', d')$. If $\frac{{d'}}{d} = 32$, then $\frac{{P'}}{P}$ should be

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?

A monatornic gas at a pressure $P,$ having a volume $V$ expands isothermally to a volume $2\, V$ and then adiabatically to a volume $16\, V.$ The final pressure of the gas is $(\,Take \,\gamma = 5/3)$

A cyclic process $ABCA$ is shown in $PT$ diagram. When presented on $PV$, it would

One mole of an ideal monoatomic gas undergoes the following four reversible processes:

Step $1$ It is first compressed adiabatically from volume $8.0 \,m ^{3}$ to $1.0 \,m ^{3}$.

Step $2$ Then expanded isothermally at temperature $T_{1}$ to volume $10.0 \,m ^{3}$.

Step $3$ Then expanded adiabatically to volume $80.0 \,m ^{3}$.

Step $4$ Then compressed isothermally at temperature $T_{2}$ to volume $8.0 \,m ^{3}$.

Then, $T_{1} / T_{2}$ is