What is the correct relationship between changes in enthalpy and internal energy within the following options?
1. \(\mathrm{\Delta {H}+\Delta {U}=\Delta {nR}} \)
2. \(\mathrm{\Delta {H}=\Delta {U -\Delta n_gRT}}\)
3. \(\mathrm{\Delta {H}=\Delta {U+\Delta n_gRT }}\)
4. \(\mathrm{\Delta {H} -\Delta {U=-\Delta n_gRT}}\)

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

For irreversible expansion of an ideal gas under isothermal conditions, 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. $∆\mathrm{U}\ne 0,<mspace\; width="1em"></mspace>∆{\mathrm{S}}_{\mathrm{total}}\ne 0$