Thermodynamics Questions

A gas mixture consists of $2$ moles of ${\text{O}}_2$ and $4$ moles of $\text{Ar}$ at temperature $T$. Neglecting all vibrational modes, the total internal energy of the system is:

Thermodynamic processes are indicated in the following diagram.

Match the following:

A Carnot engine having an efficiency of $\frac{1}{10}$ as heat engine, is used as a refrigerator. If the work done on the system is $10\text{J}$, the amount of energy absorbed from the reservoir at lower temperature is:

A gas is allowed to expand in a well insulated container against a constant external pressure of $2.5\text{atm}$ from an initial volume of $2.50\text{L}$ to a final volume of $4.50\text{L}$. The change in internal energy $\Delta U$ of the gas in joules will be:

For a given reaction, $\Delta H=35.5{\text{kJ mol}}^{-1}$ and $\Delta S=83.6{\text{JK}}^{-1}{\text{mol}}^{-1}$. The reaction is spontaneous at (Assume that $\Delta H$ and $\Delta S$ do not vary with temperature):