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Given below are two statements:
Statement I: When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.
Statement II: At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point.
In the light of the above statements, choose the correct answer from the options given below:

The standard enthalpy and standard entropy of decomposition of \( \mathrm{N_2O_4} \) to \( \mathrm{NO_2} \) are \( 55.0 \, \text{kJ mol}^{-1} \) and \( 175.0 \, \text{J /K}^{}/\text{ mol}^{} \) respectively. The standard free energy change for this reaction at \( 25^\circ \text{C} \) in \( \text{J mol}^{-1} \) is _________ (Nearest integer).

\( 500 \, \text{J} \) of energy is transferred as heat to \( 0.5 \, \text{mol} \) of Argon gas at \( 298 \, \text{K} \) and \( 1.00 \, \text{atm} \). The final temperature and the change in internal energy respectively are: Given: \( R = 8.3 \, \text{J K}^{-1} \, \text{mol}^{-1} \)

At the sea level, the dry air mass percentage composition is given as nitrogen gas: \( 70.0 \), oxygen gas: \( 27.0 \) and argon gas: \( 3.0 \). If total pressure is \( 1.15 \) atm, then calculate the ratio of following respectively:
(i) partial pressure of nitrogen gas to partial pressure of oxygen gas
(ii) partial pressure of oxygen gas to partial pressure of argon gas
(Given: Molar mass of N, O and Ar are \( 14 \), \( 16 \) and \( 40 \, \mathrm{g \, mol^{-1}} \) respectively.)

The effect of temperature on spontaneity of reactions are represented as:

\( \Delta H \)	\( \Delta S \)	Temperature	Spontaneity
(A) \( + \)	\( - \)	any \( T \)	Non spontaneous
(B) \( + \)	\( + \)	low \( T \)	Spontaneous
(C) \( - \)	\( - \)	low \( T \)	Non spontaneous
(D) \( - \)	\( + \)	any \( T \)	Spontaneous

The incorrect combinations are:

One mole of an ideal gas expands isothermally and reversibly from \( 10 \, \text{dm}^3 \) to \( 20 \, \text{dm}^3 \) at \( 300 \, \text{K} \). \( \Delta U \), \( q \) and work done in the process respectively are
Given: \( R = 8.3 \, \text{J K}^{-1} \text{mol}^{-1} \)
\( \ln 10 = 2.3 \)
\( \log 2 = 0.30 \)
\( \log 3 = 0.48 \)

Two vessels \( A \) and \( B \) are connected via stopcock. The vessel \( A \) is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel \( A \) expands into vessel \( B \) and no change in temperature is observed in the thermometer. Which of the following statement is true?

Consider the following data:
Heat of formation of \( \mathrm{CO_2(g)} = -393.5 \, \mathrm{kJ\,mol^{-1}} \)
Heat of formation of \( \mathrm{H_2O(l)} = -286.0 \, \mathrm{kJ\,mol^{-1}} \)
Heat of combustion of benzene \( = -3267.0 \, \mathrm{kJ\,mol^{-1}} \)
The heat of formation of benzene is __________ \( \mathrm{kJ\,mol^{-1}} \).
(Nearest integer)

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?

10.

Which of the following properties will change when system containing solution \( 1 \) will become solution \( 2 \)?

11.

A liquid when kept inside a thermally insulated closed vessel at \( 25^\circ \mathrm{C} \) was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters?

12.

Match List - \( 1 \) with List - \( 11 \).

List – I (Partial Derivatives)	List – II (Thermodynamic Quantity)
(A) \( \left( \frac{\partial G}{\partial T} \right)_P \)	(I) \( Cp \)
(B) \( \left( \frac{\partial H}{\partial T} \right)_P \)	(II) \( -S \)
(C) \( \left( \frac{\partial G}{\partial P} \right)_T \)	(III) \( Cv \)
(D) \( \left( \frac{\partial U}{\partial T} \right)_V \)	(IV) \( V \)

Choose the correct answer from the options given below:

13.

Heat treatment of muscular pain involves radiation of wavelength of about \( 900 \ \text{nm} \). Which spectral line of H atom is suitable for this?
Given: Rydberg constant \( R_H = 10^5 \ \text{cm}^{-1} \), \( h = 6.6 \times 10^{-34} \ \text{J s} \), \( c = 3 \times 10^8 \ \text{m/s} \)

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