Select the correct statement for work, heat, and change in internal energy.

$A$ gas expands with temperature according to the relation,$V=k T^{2/3}$,where $k$ is a constant. Work done when the temperature changes by $60 \ K$ is ($R=$ universal gas constant.) (in $R$)

$A$ gas of mass '$m$' and molecular weight '$M$' is flowing in an insulated tube with a velocity '$2V$'. If the flow of the gas is suddenly stopped and all the kinetic energy is utilized to compress the gas,the increase in the temperature of the gas is ($\gamma$ is the ratio of specific heats,$R$ is the universal gas constant).

Obtain the relation between the coefficient of performance and the efficiency of a heat engine.

One mole of a gas expands obeying the relation as shown in the $P-V$ diagram. The maximum temperature in this process is equal to

An ideal gas with constant heat capacity $C_V = \frac{3}{2} n R$ is made to carry out a cycle that is depicted by a triangle in the figure given below. The following statement is true about the cycle.