Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A $$ \to $$ B, A $$ \to $$ C and A $$ \to $$ D. The change in internal energies during these process are taken as E_AB, E_AC and E_AD and the work done as W_AB, W_AC and W_AD.
The correct relation between these parameters are :

Number of molecules in a volume of 4 cm³ of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to?
(Given, mean kinetic energy of a molecule
(at T) is 4 $$ \times $$ 10^–14 erg, g = 980 cm/s², density of
mercury = 13.6 g/cm³)

Match the thermodynamic processes taking place in a system with the correct conditions. In the table : $$\Delta $$Q is the heat supplied, $$\Delta $$W is the work done and $$\Delta $$U is change in internal energy of the system.

Process	Condition
(I) Adiabatic	(1) $$\Delta $$W = 0
(II) Isothermal	(2) $$\Delta $$Q = 0
(III) Isochoric	(3) $$\Delta $$U $$ \ne $$ 0, $$\Delta $$W $$ \ne $$ 0, $$\Delta $$Q $$ \ne $$ 0
(IV) Isobaric	(4) $$\Delta $$U = 0

The specific heat of water
= 4200 J kg^-1K^-1 and the latent heat of
ice = 3.4 $$ \times $$ 10⁵ J kg^–1. 100 grams of ice at
0^oC is placed in 200 g of water at 25^oC. The
amount of ice that will melt as the temperature
of water reaches 0^oC is close to (in grams) :