Which of the following options correctly represents the relationship between \(C_p \text { and } C_V\) for one mole of an ideal gas?

1.	\(C_P=R C_V \)	2.	\(C_V=RC_P \)
3.	\(C_P+C_V=R \)	4.	\(C_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}\)

For irreversible expansion of an ideal gas under isothermal condition, the correct option is :

1. $∆\mathrm{U}=0, ∆{\mathrm{S}}_{\mathrm{total}}\ne 0$

2. $∆\mathrm{U}\ne 0, ∆{\mathrm{S}}_{\mathrm{total}}=0$

3. $∆\mathrm{U}=0, ∆{\mathrm{S}}_{\mathrm{total}}=0$

4. $∆\mathrm{U}\ne 0, ∆{\mathrm{S}}_{\mathrm{total}}\ne 0$

Two litres of 1 mol an ideal gas at a pressure of 10 atm expands isothermally at 25 °C into a vacuum until its total volume is 10 litres. The amount of heat absorbed during expansion is:
(Given: The same expansion, for 1 mol of an ideal gas conducted reversibly.
log 5 = 0.699)

1. 51. 39 atm L

2. 39.36 atm L

3. 37. 34 atm ml

4. 26. 49 atm L

Assuming the water vapour to be a perfect gas. When 1 mol of water at 100°C and 1 bar pressure is converted to ice at 0°C, the change in internal energy is-

(The enthalpy of fusion of ice = 6.00 kJ mol^-1 , heat capacity of water = 4.2 J/g°C)

1. 13.56 kJ mol^-1

2. -12.16 kJ mol^-1

3. -13.56 kJ mol^-1

4. 12.16 kJ mol^-1

What is the nature of the reaction depicted in the given diagram for A→C?

Consider the following diagram for a reaction $\mathrm{A}\to \mathrm{C}$. 

The nature of the reaction is-

1. Exothermic

2. Endothermic

3. Reaction at equilibrium

4. None of the above

Consider the following graph.

The work done, as per the graph above, is:

For the graph given below, it can be concluded that work done during the process shown will be-

The entropy change in the surroundings when 1.00 mol of H₂O_(l) is formed under standard conditions is:

∆_fH^θ = –286 kJ mol^–1 

1. 952.5 J mol^-1

2. $979.7$ $\mathrm{J}$ ${\mathrm{mol}}^{-1}$

3. $949.7$ $\mathrm{J}$ ${\mathrm{mol}}^{-1}$

4. $959.7$ $\mathrm{J}$ ${\mathrm{mol}}^{-1}$

$\frac{1}{2}{N_2}_{ \left(\mathrm{g}\right)} + \frac{1}{2}{O}_{2 \left(\mathrm{g}\right)} \to N{O}_{\left(\mathrm{g}\right)} ;$
${∆}_{\mathrm{r}}H° = 90 kJ mo{l}^{-1}$
$N{O}_{\mathit{\left(}g\mathit{\right)}} + \frac{1}{2}{O_2}_{\mathit{\left(}g\mathit{\right)}} \to N{O_{\mathit{2}}}_{\mathit{\left(}g\mathit{\right)}}\hspace{0.17em};$
${∆}_{\mathrm{r}}\mathrm{H}° = -74 \mathrm{kJ} {\mathrm{mol}}^{-1}$

The thermodynamic stability of NO_(g) based on the above data is:

1. Less than NO_2(g) 

2. More than NO_2(g)

3. Equal to NO_2(g)

4. Insufficient data