The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal mono atomic gas. The amount of heat, extracted from the source in a single cycle is 

One mole of diatomic ideal gas undergoes a cyclic process $\mathrm{ABC}$ as shown in figure. The process $\mathrm{BC}$ is adiabatic. The temperatures at $A, B$ and $C$ are $400\mathrm{K}, 800\mathrm{K}$ and $600 \mathrm{K}$, respectively. Choose the correct statement.

A solid of constant heat capacity $1 \mathrm{J}{}^{\circ }\mathrm{C}^{-1}$ is being heated by keeping it in contact with reservoirs in two ways :

(i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat.

(ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies the same amount of heat. In both the cases body is brought from initial temperature $100°\mathrm{C}$ to final $200°\mathrm{C}$. Entropy change of the body in the two cases respectively is :
 

A thermally insulated, the closed copper vessel contains water at $15 °\mathrm{C}$. When the vessel is shaken vigorously for $15 \min$, the temperature rises to $17 °\mathrm{C}$. The mass of the vessel is $100 \mathrm{g}$ and that of the water is $200 \mathrm{g}$. The specific heat capacities of copper and water are $420 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ and $4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$, respectively. Neglect any thermal expansion.

$\left(\mathrm{a}\right)$ How much heat is transferred to the liquid-vessel system?

$\left(\mathrm{b}\right)$ How much work has been done on this system?

$\left(\mathrm{c}\right)$ How much is the increase in internal energy of the system?

One gram of water $\left(\mathrm{volume}=1 {\mathrm{cm}}^3\right)$ becomes $1671 {\mathrm{cm}}^3$ of steam when boiled at a pressure of one atmosphere. Latent heat of vaporization at this pressure is $539 \mathrm{cal} {\mathrm{gm}}^{-1}$. Compute the work done. $\left[1 \mathrm{atm}=1.013\times {10}^5 \mathrm{N} {\mathrm{m}}^{-2}\right]$

Two moles of an ideal monoatomic gas are contained in a vertical cylinder of cross-sectional area $A$ as shown in the figure. The piston is frictionless and has a mass $m$. At a certain instant a heater starts supplying heat to the gas at a constant rate $q \mathrm{J} {\mathrm{s}}^{-1}$. Find the steady velocity of the piston under isobaric condition. All the boundaries are thermally insulated.