$10,000$ small balls,each of mass $1 \, g$,strike a surface of area $1 \, cm^2$ per second with a velocity of $100 \, m/s$ perpendicular to the surface. They rebound with the same velocity. What is the pressure exerted on the surface?

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,$\frac{dP}{P} = .........$

The internal energy of an ideal diatomic gas corresponding to volume $V$ and pressure $P$ is $2.5 PV$. The gas expands from $1 \text{ litre}$ to $2 \text{ litre}$ at a constant pressure of $10^5 \text{ N/m}^2$. The heat supplied to the gas is: (in $\text{ J}$)

In the figure,a container is shown to have a movable (frictionless) piston on top. The container and the piston are made of perfectly insulating material,allowing no heat transfer between the outside and inside. The container is divided into two compartments by a rigid partition made of a thermally conducting material that allows slow heat transfer. The lower compartment is filled with $2$ moles of an ideal monatomic gas at $700 \ K$,and the upper compartment is filled with $2$ moles of an ideal diatomic gas at $400 \ K$. The heat capacities per mole are: for monatomic gas,$C_v = \frac{3}{2} R, C_p = \frac{5}{2} R$; for diatomic gas,$C_v = \frac{5}{2} R, C_p = \frac{7}{2} R$.
$1.$ Consider the partition to be rigidly fixed so that it does not move. When equilibrium is achieved,the final temperature of the gases will be:
$(A) 550 \ K$ $(B) 525 \ K$ $(C) 513 \ K$ $(D) 490 \ K$
$2.$ Now consider the partition to be free to move without friction so that the pressure of gases in both compartments is the same. Then the total work done by the gases until they achieve equilibrium will be:
$(A) 250 \ R$ $(B) 200 \ R$ $(C) 100 \ R$ $(D) -100 \ R$
Give the answer for questions $1$ and $2$.

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is $4 \text{ cm}^2$. The gas is heated slowly to raise the temperature by $1.2^\circ\text{C}$ during which the piston moves by $25 \text{ mm}$. The amount of heat supplied to the gas is . . . . . . $J$. (Atmospheric pressure = $100 \text{ kPa}$, $R = 8.3 \text{ J/mol}\cdot\text{K}$) (Neglect mass of the piston)

One mole of an ideal monoatomic gas undergoes the process $A \rightarrow B \rightarrow C \rightarrow D \rightarrow A$ as shown in the graph. The work done during the process is