\(q_{rev}= (-\Delta_f H^{\ominus})=-286 kJ\ mol^{-1}=286000\ J\ mol^{-1}\)
\(\Delta{S}{_{(Surroundmgs)}}=\frac{q_{rev}}{T}=\frac{286000\ J\ mol^{-1}}{298\ K}\) = 959 J K^-1 mol^-1.

\(\Delta { G }^{ \ominus }\) = -RT ln K = -2.303 RT log K.
R = 8.314 JK^-1 mol^-1;T = 300 K; K=10
\(\Delta { G }^{ \ominus }=-2.303 \times 8.314 \)  JK^-1 mol^-1 x (300 K) x log 10
= -5527 J mol^-1= -5.527 kJ mol^-1

ΔG⁰ = - 2.303 RT log k_c
= - 2.303 x 8.314 x 298 log (1.8 x 10^-7)
= - 38484 J mol^-1
= - 38.484 kJ mol-1

Δ H⁰= ΔU⁰ + RT(Δn)
= -10.5 + 8.314 x 10^-3 x 298 x (-1)
= -12.978 kJ
We know, ΔG⁰= Δ H⁰ - TΔS⁰ 
= -12.978 - 298 (- 44.1 x 10^-3)
= 0.164 kJ
Hence, the reaction is non spontaneous.

In the reaction 2NaHCO₃(s) \(\rightarrow\) Na₂CO₃(s) +CO₂(g) + H₂O(g) the number of gaseous components increase and hence entropy of the system will increase.

When a crystalline solid is heated from 0K to 115K, the entropy increases (\(\triangle\)S = positive) because at higher temperature, the constituent units starts vibrating around their mean position.

(i) The heat of formation of compounds can be calculated from heat of combustion values.
(ii) The calorific value of food and fuels can be calculated from heat of combustion.

At constant pressure processes, a system has to do work against the surroundings. Hence, the system would require more heat to effect a given temperature rise than at constant volume, so C_p is always greater than C_v.

(i) The heat capacity at constant volume (C_v) is defined as the rate of change of internal energy with respect to temperature at constant volume.
\({ C }_{ v }={ \left( \frac { \partial H }{ \partial T } \right) }_{ v }\)
(ii) The molar heat capacity at constant pressure (C_p ) can be defined as the rate of change of enthalpy with respect to temperature at constant pressure.
\({ C }_{ P }={ \left( \frac { \partial H }{ \partial T } \right) }_{ P }\)

It is impossible to construct a machine that absorbs heat from a hot source and converts it completely into work by a cyclic process without transferring a part of heat to a cold sink

Lattice energy is defined as "The amount of energy required to completely remove the constituent ions from its crystal lattice to an infinite distance." It is also referred as lattice enthalpy

The heat of neutralisation is defined as "The change in enthalpy when one gram equivalent of an acid is completely neutralised by one gram equivalent of a base or vice versa in dilute solution"

The calorific value is defined as "The amount of heat produced in calories (or joules) when one gram of the substance is completely burnt." The SI unit of calorific value is J kg^-1. It is usually expressed in cal g ^-1.

Molar heat capacity is defined as "The amount of heat absorbed by one 'mole of the substance to raise its temperature by 1 kelvin". The SI unit of molar heat capacity is JK^-1 mol^-1

Given
T₁ = 127°C = 127 + 273 = 400 K
T = 47°C = 47 + 273 = 320 K
% efficiency η = ?
η = \(\left[ \frac { { T }_{ 1 }-{ T }_{ 2 } }{ { T }_{ 1 } } \right] \) x 100
η =\(\left[ \frac { 400-320 }{ 400 } \right] \) x 100
η = \(\left[ \frac { 80 }{ 400 } \right] \) x 100
η = 20%