Two moles of helium gas are taken over the cycle $ABCDA$, as shown in the $P-T$ diagram. The net work done on the gas in the cycle $ABCDA$ is ...... $R$.

Fill in the blanks:
$1.$ The heat required to raise the temperature of a body by $1\,K$ is called ...... .
$2.$ $A$ temperature difference of $10\,^{\circ}C$ is equivalent to a temperature difference of ...... on the Fahrenheit temperature scale.
$3.$ For an isothermal process of an ideal gas,$\frac{dP}{P} = .........$

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.

Two cylinders $A$ and $B$ fitted with pistons contain an equal amount of an ideal rigid diatomic gas at $303 \ K$. The piston of cylinder $A$ is free to move,and that of cylinder $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in cylinder $B$ is $49 \ K$,then the rise in temperature of the gas in $A$ is: (in $K$)

Carbon monoxide is carried around a closed cycle $abc$ in which $bc$ is an isothermal process as shown in the figure. The gas absorbs $7000 \; J$ of heat as its temperature increases from $300 \; K$ to $1000 \; K$ in going from $a$ to $b$. The quantity of heat rejected by the gas during the process $ca$ is ..... $J$. (in $; J$)

There are two samples $A$ and $B$ of a certain gas,which are initially at the same temperature and pressure. Both are compressed from volume $V$ to $\frac{V}{2}$. Sample $A$ is compressed isothermally while sample $B$ is compressed adiabatically. The final pressure of $A$ is