$A$ gas expands such that its initial and final temperatures are equal. Also,the process followed by the gas traces a straight line on the $P-V$ diagram:

When $Q_1$ amount of heat is supplied to a monatomic gas,the work done by the gas is $W$. When $Q_2$ amount of heat is supplied to a diatomic gas,the work done by the gas is $2W$. Then $Q_1: Q_2=$

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4 \text{ cm}^2$. The gas is heated slowly to raise the temperature by $1.2^\circ\text{C}$ during which the piston moves by $25 \text{ mm}$. The amount of heat supplied to the gas is . . . . . . $J$. (Atmospheric pressure = $100 \text{ kPa}$,$R = 8.3 \text{ J/mol}\cdot\text{K}$) (Neglect mass of the piston)

$A$ thermodynamic system goes from states $(i) \, P_1, V$ to $2P_1, V$ and $(ii) \, P, V$ to $P, 2V$. The work done in the two cases is:

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then is compressed to the original volume $V_1$ adiabatically. The initial pressure is $P_1$ and the final pressure is $P_3$. If the total work done is $W$,then:

The $VT$ curve for a thermodynamic process is given. Identify the corresponding $PV$ curve.