$A$ 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 $x$.

Which of the following statement$(s)$ is/are true? "Internal energy of an ideal gas ..........."

What is an isochoric process and a cyclic process? Write the first law of thermodynamics for an ideal gas.

Which of the following statements is correct?

$A$ cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in the figure. Find the heat exchanged by the engine with the surroundings for each section of the cycle. Given ${C_v} = \frac{3}{2}R$.
$(a)$ $A$ to $B$: constant volume
$(b)$ $B$ to $C$: constant pressure
$(c)$ $C$ to $D$: adiabatic
$(d)$ $D$ to $A$: constant pressure

$A$ gas is compressed from a volume of $2 \,m^3$ to a volume of $1 \,m^3$ at a constant pressure of $100 \,N m^{-2}$. Then it is heated at constant volume by supplying $150 \,J$ of energy. As a result,the internal energy of the gas