An ideal gas undergoes a cyclic process as shown in the $P-V$ diagram. The work done by the gas in the complete cycle is:

Calculate change in internal energy when 5 mole of hydrogen is heated to ${20^ \circ }C$from ${10^ \circ }C$, specific heat of hydrogen at constant pressure is 8 cal ${\left( {{\rm{mol^\circ C}}} \right)^{ - 1}}$

Which of the following thermodynamic processes involves no heat exchange with the surroundings?

A gas is compressed isothermally to one-third its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to one-third. Which of the following statements is true?

In an isothermal reversible expansion, if the volume of $96g$ of oxygen at ${27^ \circ }C$ is increased from $70litres$ to $140litres$, then the work done by the gas will be

A monoatomic ideal gas at 300 K is compressed isothermally to half its initial volume. The same gas, starting at the same initial conditions, is compressed adiabatically to half its initial volume. What is the final temperature of the gas in the adiabatic process?

If for hydrogen ${C_p} - {C_v} =$ $m$ and for the nitrogen ${C_p} - {C_v} =$ $n$, where ${C_p},{C_v}$ refer to specific heats per unit mass respectively at constant pressure and constant volume, the relation between $m$ and $n$ is

One mole of an ideal gas requires 207 J heat to raise the temperature by 1K, when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same range, the heat required will be ($R = 8.3{\rm{Jmo}}{{\rm{l}}^{ - 1}}{{\rm{K}}^{ - 1}})$)

$80gm$ of water at ${30^{\rm{o}}}C\,\,$ are poured on a large block of ice at ${0^{\rm{o}}}C$ The mass of ice that melts is

A gas undergoes a process described by $P = \frac{a}{V} + b$, where $a$ and $b$ are constants. The work done by the gas when the volume changes from $V_1$ to $V_2$ is:

In an isothermal reversible expansion, if the volume of $96g$ of oxygen at ${27^ \circ }C$ is increased from $70litres$ to $140litres$, then the work done by the gas will be