Consider the following statements:
$A$. Zeroth law of thermodynamics gives the concept of temperature.
$B$. First law of thermodynamics gives the concept of internal energy.
$C$. In isothermal expansion of an ideal gas, $\Delta Q \neq \Delta W$.
$D$. The product of intensive and extensive variables is extensive.
$E$. The ratio of any extensive variable to mass will be an extensive variable.
Choose the correct combination of statements from the options given below:

$A$ gas is compressed from a volume of $2 \,m^3$ to a volume of $1 \,m^3$ at a constant pressure of $100 \,N m^{-2}$. Then it is heated at constant volume by supplying $150 \,J$ of energy. As a result,the internal energy of the gas

$A$ cyclic process $ABCD$ is shown in the given $P-V$ diagram. Which of the following diagrams represents the same process in a $P-T$ graph?

Match the "Technology" given in List-$1$ with the "Principle of Physics" given in List-$2$.

$A$. Steam engine	$I$. Magnetic confinement of plasma
$B$. Electron microscope	$II$. Laws of thermodynamics
$C$. Non-reflecting coatings	$III$. Wave nature of electrons
$D$. Tokamak	$IV$. Interference of light

$A$ cyclic process $ABCD$ is shown in the $P-V$ diagram. Which of the following curves represent the same process?

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 $2$.