Figure shows a cylindrical adiabatic container of total volume $2V_0$ divided into two equal parts by a conducting piston (which is free to move). Each part containing identical gas at pressure $P_0$ . Initially temperature of left and right part is $4T_0$ and $T_0$ respectively. An external force is applied on the piston to keep the piston at rest. Find the value of external force required when thermal equilibrium is reached. ( $A =$ Area of piston)

Adiabatic modulus of elasticity of a gas is $2.1 \times {10^5}N/{m^2}.$ What will be its isothermal modulus of elasticity $\left( {\frac{{{C_p}}}{{{C_v}}} = 1.4} \right)$

A gas at initial temperature $T$ undergoes sudden expansion from volume $V$ to $2 \,V$. Then,

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

$P-V$ plots for two gases during adiabatic process are shown in the figure. Plots $1$ and $2$ should correspond respectively to

Two moles of an ideal monoatomic gas occupies a volume $V$ at $27^o C$. The gas expands adiabatically to a volume $2\ V$. Calculate $(a)$ the final temperature of the gas and $(b)$ change in its internal energy.