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For complete combustion of ethene, \( \mathrm{C_2H_4(g)} + \mathrm{3O_2(g)} \longrightarrow \mathrm{2CO_2(g)} + \mathrm{2H_2O(l)} \) the amount of heat produced as measured in bomb calorimeter is \( 1406 \, \mathrm{kJ\, mol^{-1}} \) at \( 300 \, \mathrm{K} \). The minimum value of \( \mathrm{T\Delta S} \) needed to reach equilibrium is (–) ________ \( \mathrm{kJ} \) (Nearest integer)
Given: \( R = 8.3 \, \mathrm{J\,K^{-1}\,mol^{-1}} \)

When a \( 60 \, \text{W} \) electric heater is immersed in a gas for \( 100 \, \text{s} \) in a constant volume container with adiabatic walls, the temperature of the gas rises by \( 5^\circ \text{C} \). The heat capacity of the given gas is ________ \( \text{J K}^{-1} \). (Nearest integer)

The total number of intensive properties from the following is ________ Volume, Molar heat capacity, Molarity \( E^{\ominus} \) cell, Gibbs free energy change. Molar mass. Mole

One mole of an ideal monoatomic gas is subjected to changes as shown in the graph. The magnitude of the work done (by the system or on the system) is ___________ \( \mathrm{J} \). (nearest integer)

Given: \( \log 2 = 0.3 \)
\( \ln 10 = 2.3 \)

Which of the following relations are correct?
(A) \( \Delta U = q + p\Delta V \)
(B) \( \Delta G = \Delta H - T\Delta S \)
(C) \( \Delta S = \frac{q_{rev}}{T} \)
(D) \( \Delta H = \Delta U - \Delta nRT \)
Choose the most appropriate answer from the options given below:

One mole of an ideal gas at \( 350 \, \text{K} \) is in a \( 2.0 \, \text{L} \) vessel of thermally conducting walls, which are in contact with the surroundings. It undergoes isothermal reversible expansion from \( 2.0 \, \text{L} \) to \( 3.0 \, \text{L} \) against a constant pressure of \( 4 \, \text{atm} \). The change in entropy of the surrounding (\( \Delta S \)) is ______ \( \text{J K}^{-1} \) (Nearest integer) Given \( R = 8.314 \, \text{J K}^{-1} \, \text{mol}^{-1} \)

\( 30.4 \ \text{kJ} \) of heat is required to melt one mole of sodium chloride and the entropy change at the melting point is \( 28.4 \ \text{J K}^{-1} \text{ mol}^{-1} \) at \( 1 \ \text{atm} \). The melting point of sodium chloride is ________ \( \text{K} \) (Nearest Integer)

When \( 2 \, \text{litre} \) of ideal gas expands isothermally into vacuum to a total volume of \( 6 \, \text{litre} \), the change in internal energy is ________ \( \text{J} \). (Nearest integer)

For independent processes at \( 300 \, \text{K} \)

The number of non-spontaneous processes from the following is ____________.

\( 1 \) mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of \( 27^\circ \mathrm{C} \). The work done is \( 3 \, \mathrm{kJ\,mol^{-1}} \). The final temperature of the gas is ________ \( \mathrm{K} \) (Nearest integer). (Given \( C_V = 20 \, \mathrm{J\,mol^{-1}\,K^{-1}} \) )

For \( 1 \) mol of gas, the plot of \( pV \) vs. \( p \) is shown below. \( p \) is the pressure and \( V \) is the volume of the gas

What is the value of compressibility factor at point A?

What happens when methane undergoes combustion in systems A and B respectively?

An athlete is given \(100 \ \mathrm{g}\) of glucose \( (\mathrm{C_6H_{12}O_6}) \) for energy. This is equivalent to \(1800 \ \mathrm{kJ}\) of energy. The \(50\%\) of this energy gained is utilized by the athlete for sports activities at the event. In order to avoid storage of energy, the weight of extra water he would need to perspire is ______ \( \mathrm{g} \) (Nearest integer)
Assume that there is not other way of consuming stored energy.
Given: The enthalpy of evaporation of water is \(45 \ \mathrm{kJ \ mol^{-1}}\)
Molar mass of \( \mathrm{C, H \ \& \ O} \) are \(12\), \(1\) and \(16 \ \mathrm{g \ mol^{-1}}\).

Consider the graph of Gibbs free energy \( G \) vs Extent of reaction. The number of statements from the following which are true with respect to points \( (a) \), \( (b) \) and \( (c) \) is __________,

\((1)\) Reaction is spontaneous at \( (a) \) and \( (b) \)
\((2)\) Reaction is at equilibrium at point \( (b) \) and non-spontaneous at point \( (c) \)
\((3)\) Reaction is spontaneous at \( (a) \) and non-spontaneous at \( (c) \)
\((4)\) Reaction is non-spontaneous at \( (a) \) and \( (b) \)

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JEE Main 2023 24th Jan Morning Shift

For independent processes at \( 300 \, \text{K} \)

The number of non-spontaneous processes from the following is ____________.