In changing the state of a gas adiabatically from an equilibrium state $A$ to another equilibrium state $B$,an amount of work equal to $22.3 \; J$ is done on the system. If the gas is taken from state $A$ to $B$ via a process in which the net heat absorbed by the system is $9.35 \; cal$,how much is the net work done (in $J$) by the system in the latter case? (Take $1 \; cal = 4.19 \; J$)

The ratio of the slopes of isothermal and adiabatic curves is

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:

$A$ soap bubble of radius $r$ contains a monoatomic ideal gas. The gas is heated in such a manner that the bubble remains in mechanical equilibrium. Assuming that the soap material of the bubble has no heat capacity,the molar heat capacity of the gas in the process will be (Neglect atmospheric pressure). (in $R$)

The cycle shown in the figure represents an engine (the engine consists of one mole of gas in a cylinder with a piston). $A$ to $B$ is isochoric,$B$ to $C$ is isothermal,$C$ to $D$ is isochoric,and $D$ to $A$ is isothermal. Also,$V_C = V_D = 2V_A = 2V_B$.
$(a)$ In which part of the cycle is heat supplied to the engine from the outside?
$(b)$ In which part of the cycle can the engine give energy to its surroundings?
$(c)$ How much work is done by the engine during one cycle? Give your answer in terms of $P_A, P_B$ and $V_A$.
$(d)$ What is the efficiency of the engine? (For the gas,$\gamma = 5/3$,and for one mole,$C_V = 3/2 R$)

What is the specific heat of a gas in an isothermal process and an adiabatic process?