If $\Delta U$ and $\Delta W$ represent the increase in internal energy and work done by the system respectively in a thermodynamic process, which of the following is true?

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  …. $kJ$

A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac {1}{6}$ . When $T_2$ is lowered by $60\,K$ ; its efficiency increases to $\frac {1}{3}$. Then $T_1$ and $T_2$ are respectively

$5.6\, liter$ of helium gas at $STP$ is adiabatically compressed to $0.7\, liter$. Taking the initial temperature to be $T_1$, the magnitude work done in the process is

A perfect gas is found to obey the relation $PV^{3/2} =$ constant, during an adiabatic process. If such a gas, initially at a temperature $T$, is compressed adiabatically to half its initial volume, then its final temperature will be