The work done when 1 mole of gas expands reversibly and isothermally from a pressure of 5 atm to 1 atm at 300 K is: ​
(Given log 5 = 0.6989 and R = 8.314 J K^-1 mol^-1)
1. zero J
2. 150 J
3. +4014.6 J
4.-4014.6 J

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

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

1. $∆\mathrm{U}=0,<mspace\; width="1em"></mspace>∆{\mathrm{S}}_{\mathrm{total}}\ne 0$

2. $∆\mathrm{U}\ne 0,<mspace\; width="1em"></mspace>∆{\mathrm{S}}_{\mathrm{total}}=0$

3. $∆\mathrm{U}=0,<mspace\; width="1em"></mspace>∆{\mathrm{S}}_{\mathrm{total}}=0$

4. $∆\mathrm{U}\ne 0,<mspace\; width="1em"></mspace>∆{\mathrm{S}}_{\mathrm{total}}\ne 0$

Hydrolysis of sucrose is given by the following reaction

Sucrose + H₂O $\rightleftharpoons$ Glucose + Fructose

If the equilibrium constant (K_c) is 2$\times$10¹³ at 300 K, the value of ${∆}_r{G}^{⊝}$ at the same temperature will be:

1. 8.314 J mol^–1 K^–1$\times$300 K$\times$ln (2$\times$10¹³)

2. 8.314 J mol^–1 K^–1$\times$300 K$\times$ln (3$\times$10¹³)

3. –8.314 J mol^–1 K^–1$\times$300 K$\times$ln (4$\times$10¹³)

4. –8.314 J mol^–1 K^–1$\times$300 K$\times$ln (2$\times$10¹³)

For the reaction, 2Cl(g) $\to$ Cl₂(g), the correct option is:

1. ${∆}_{\mathrm{r}}\mathrm{H}>0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{∆}_{\mathrm{r}}\mathrm{S}<0$

2. ${∆}_{\mathrm{r}}\mathrm{H}<0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{∆}_{\mathrm{r}}\mathrm{S}>0$

3. ${∆}_{\mathrm{r}}\mathrm{H}<0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{∆}_{\mathrm{r}}\mathrm{S}<0$

4. ${∆}_{\mathrm{r}}\mathrm{H}>0<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>{∆}_{\mathrm{r}}\mathrm{S}>0$

The correct option for free expansion of an ideal gas under adiabatic condition is:

1.  $q=0,$ $∆T<0$ and $w>0$

2.  $q<0,$ $∆T=0$ and $w=0$

3.  $q>0,$ $∆T>0$ and $w>0$

4.  $q=0,$ $∆T=0$ and $w=0$