One mole of a monoatomic gas and one mole of a diatomic gas are initially in the same state. Both gases are expanded isothermally and then adiabatically,such that they acquire the same final state. Choose the correct statement.

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

$A$ gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure $P_i = 10^5 \text{ Pa}$ and volume $V_i = 10^{-3} \text{ m}^3$ changes to a final state at $P_f = (1/32) \times 10^5 \text{ Pa}$ and $V_f = 8 \times 10^{-3} \text{ m}^3$ in an adiabatic quasi-static process, such that $P^3 V^5 = \text{constant}$. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at $P_i$, followed by an isochoric (isovolumetric) process at volume $V_f$. The amount of heat supplied to the system in the two-step process is approximately: (in $\text{ J}$)

$A$ process is shown in the diagram. Which of the following curves may represent the same process?

$A$ 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:

$A$ bubble containing $8$ moles of Helium is submerged at a certain depth in water. When the temperature of the water increases by $30 \ ^\circ C$,how much heat in $J$ is added during the expansion of the Helium bubble?