In thermodynamics,heat and work are

An ideal gas at initial temperature $T_0$ and initial volume $V_0$ is expanded adiabatically to a volume $2 V_0$. The gas is then expanded isothermally to a volume $5 V_0$ and thereafter compressed adiabatically so that the temperature of the gas becomes again $T_0$. If the final volume of the gas is $\alpha V_0$,then the value of constant $\alpha$ is

One mole of a monatomic ideal gas undergoes the cyclic process $J \rightarrow K \rightarrow L \rightarrow M \rightarrow J$,as shown in the $P - T$ diagram. Match the quantities mentioned in $List-I$ with their values in $List-II$ and choose the correct option. [$R$ is the gas constant]

$List-I$	$List-II$
$(P)$ Work done in the complete cyclic process	$(1)$ $R T_0 - 4 R T_0 \ln 2$
$(Q)$ Change in the internal energy of the gas in the process $JK$	$(2)$ $0$
$(R)$ Heat given to the gas in the process $KL$	$(3)$ $3 R T_0$
$(S)$ Change in the internal energy of the gas in the process $MJ$	$(4)$ $-2 R T_0 \ln 2$
	$(5)$ $-3 R T_0 \ln 2$

When heat $Q$ is supplied to a monoatomic gas at constant pressure,the work done by the gas is:

An ideal gas with adiabatic exponent $(\gamma = 1.5)$ undergoes a process in which the work done by the gas is equal to the increase in the internal energy of the gas. The molar heat capacity of the gas for this process is:

What are the differences between mechanics and thermodynamics?