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

$A$ cylinder made of perfectly non-conducting material,closed at both ends,is divided into two equal parts by a heat-proof piston. Both parts of the cylinder contain the same mass of a gas at a temperature $t_0 = 27^{\circ}C$ and pressure $P_0 = 1 \text{ atm}$. If the gas in one of the parts is slowly heated to $t = 57^{\circ}C$ while the temperature of the first part is maintained at $t_0$,the distance moved by the piston from the middle of the cylinder will be $x \text{ cm}$. Find $x$ (total length of the cylinder $= 84 \text{ cm}$).

Two cylinders of equal size are filled with an equal amount of ideal diatomic gas at room temperature. Both cylinders are fitted with pistons. In cylinder $A$,the piston is free to move (isobaric process),while in cylinder $B$,the piston is fixed (isochoric process). When the same amount of heat is supplied to both cylinders,the temperature of the gas in cylinder $A$ rises by $30\, K$. What will be the rise in temperature of the gas in cylinder $B$ (in $;K$)?

$A$ bubble containing $8$ moles of Helium is submerged at a certain depth in water. When the temperature of the water increases by $30 \ ^\circ C$,how much heat in $J$ is added during the expansion of the Helium bubble?

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,$C_V = 3/2 R$)

$A$ cyclic process $ABCA$ is shown in the $V-T$ diagram. The corresponding process on the $P-V$ diagram is: