$540$ calories of heat converts $1$ cubic centimeter of water at $100\,^oC$ into $1671$ cubic centimeter of steam at $100\,^oC$ at a pressure of one atmosphere. Then the work done against the atmospheric pressure is nearly .......... $cal$.

$A$ quantity of heat $Q$ is supplied to a monoatomic ideal gas which expands at constant pressure. What is the fraction of heat converted into work? Given $\gamma = \frac{C_p}{C_v} = \frac{5}{3}$.

$A$ certain amount of gas is taken through a cyclic process $(A-B-C-D-A)$ that has two isobars, one isochore, and one isothermal process. The cycle can be represented on a $P-V$ indicator diagram as:

Two identical adiabatic vessels are filled with oxygen at pressure $P_1$ and $P_2$ $(P_1 > P_2)$. The vessels are interconnected with each other by a non-conducting pipe. If $U_{01}$ and $U_{02}$ denote the initial internal energy of oxygen in the first and second vessel respectively,and $U_{f1}$ and $U_{f2}$ denote the final internal energy values,then:

An insulating cylinder contains $4 \text{ moles}$ of an ideal diatomic gas. When a heat $Q$ is supplied to it,$2 \text{ moles}$ of the gas molecules dissociate. If the temperature of the gas remains constant,then the value of $Q$ is ($R$ - universal gas constant).

The efficiency of a Carnot engine operating with a hot reservoir kept at a temperature of $1000 K$ is $0.4$. It extracts $150 J$ of heat per cycle from the hot reservoir. The work extracted from this engine is being fully used to run a heat pump which has a coefficient of performance $10$. The hot reservoir of the heat pump is at a temperature of $300 K$. Which of the following statements is/are correct:
$(A)$ Work extracted from the Carnot engine in one cycle is $60 J$.
$(B)$ Temperature of the cold reservoir of the Carnot engine is $600 K$.
$(C)$ Temperature of the cold reservoir of the heat pump is $270 K$.
$(D)$ Heat supplied to the hot reservoir of the heat pump in one cycle is $540 J$.