$A$ monoatomic gas performs a work of $\frac{Q}{4}$,where $Q$ is the heat supplied to it. The molar heat capacity of the gas during this transformation will be $xR$,where $R$ is the gas constant. Find the value of $x$.

$A$ given amount of gas has an initial state $(P_i, V_i, T_i)$. It expands until its volume becomes $V_f$. Consider the following two cases:
$(a)$ The expansion occurs at constant temperature (isothermal).
$(b)$ The expansion occurs at constant pressure (isobaric).
Draw the $P-V$ diagram for each case. In which of the two cases is the work done by the gas greater?

What are the differences between mechanics and thermodynamics?

$1$ mole of rigid diatomic gas performs a work of $Q/5$ when heat $Q$ is supplied to it. The molar heat capacity of the gas during this transformation is $\frac{xR}{8}.$ The value of $x$ is $\ldots \ldots \ldots .$ $[R =$ universal gas constant $]$

In changing the state of a gas adiabatically from an equilibrium state $A$ to another equilibrium state $B$,an amount of work equal to $22.3 \; J$ is done on the system. If the gas is taken from state $A$ to $B$ via a process in which the net heat absorbed by the system is $9.35 \; cal$,how much is the net work done (in $J$) by the system in the latter case? (Take $1 \; cal = 4.19 \; J$)

If $dQ$,$dU$,and $dW$ are heat energy absorbed,change in internal energy,and external work done respectively by a diatomic gas at constant pressure,then the ratio $dW: dU: dQ$ is: