Which of the following statements is correct for an irreversible isothermal expansion of an ideal gas?

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

If for a certain reaction ${∆}_{r}H$ is 30 kJ mol^–1 at 450 K, the value of ${∆}_{r}S$ (in JK^–1 mol^–1) for which the same reaction will be spontaneous at the same temperature is:

For a sample of a perfect gas when its pressure is changed isothermally from P_i to P_f, the entropy change is given by:

1. $∆\mathrm{s}=\mathrm{nR}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{f}}}{{\mathrm{p}}_{\mathrm{i}}}\right)$

2. $∆\mathrm{s}=\mathrm{nR}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{i}}}{{\mathrm{p}}_{\mathrm{f}}}\right)$

3. $∆\mathrm{s}=\mathrm{nRT}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{f}}}{{\mathrm{p}}_{\mathrm{i}}}\right)$

4. $∆\mathrm{s}=\mathrm{RT}$ $\ln$ $\left(\frac{{\mathrm{p}}_{\mathrm{i}}}{{\mathrm{p}}_{\mathrm{f}}}\right)$