Three moles of an ideal monoatomic gas perform a cycle as shown in the figure. The gas temperature in different states are: $T_1 = 400\, K,\, T_2 = 800\, K,\, T_3 = 2400\, K$ and $T_4 = 1200\,K$ . The work done by the gas during the cycle is  .... $kJ$

During an adiabatic process, the volume of gas is found to be inversely proportional to the cube of its temperature. The ratio of $\frac{{{C_p}}}{{{C_v}}}$ for the gas is

Six moles of an ideal gas perfoms cycle shown in figure. If the temperature $T_A = 600\, K$, $T_B = 800\, K, T_C = 2200\, K$ and $T_D = 1200\, K$, the work done per cycle is........ $kJ$

Choose the incorrect statement from the following

$S1$: The efficiency of a heat engine can be $1$, but the coefficient of performance of a refrigerator can never be infinity

$S2$: The first law of thermodynamics is basically the principle of conservation of energy

$S3$: The second law of thermodynamics does not allow several phenomena consistent with the first law

$S4$: A process, whose sole result is the transfer of heat from a colder to a hotter object is impossible

In thermodynamic processes which of the following statements is not true

If $R =$ universal gas constant, the amount of heat needed to raise the temperature of $2 \,mol$ of an ideal monatomic gas from $273\, K$ to $373\, K$ when no work is done is-