A frictionless piston-cylinder based enclosure contains some amount of gas at pressure $400 \mathrm{k} \mathrm{Pa}$. Then heat is transferred to the gas at constant pressure in a quasi-static process. The piston moves at slowly through a hight of $10 \mathrm{cm}$. In the piston has a cross-section area of $0.3{ \mathrm{m}}^2$, the work done by the gas in this process is

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 :
 

An ideal monoatomic gas is confined in a horizontal cylinder by a spring loading piston (as shown in Fig $20.63$). Initially the gas is at temperature $T_1$ pressure $P_1$ and volume $V_1$ and the spring is in relaxed state. The gas is then Fig. $20.63$ heated very slowly to temperature $T_2$, pressure $p_2$ and volume $V_2$. During this process the piston moves out by a distance $X$. Ignoring the friction between the piston and the cylinder, the correct statements $\left(s\right)$ is (are)

The above $p-V$ diagram Fig. represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas. The amount of heat extracted from the source in a single cycle is :