According to Maxwell-Boltzmann distribution, the average speed of molecules of an ideal gas is given by the expression \(v_{\text{avg}} = \sqrt{\frac{8RT}{\pi M}}\).

By conservation of energy, the sum of absorptance \(a\), reflectance \(r\), and transmittance \(t\) is equal to \(1\): \(a + r + t = 1\). Therefore, \(a = 1 - \frac{1}{8} - \frac{1}{7} = 1 - \frac{15}{56} = \frac{41}{56}\).

In an adiabatic process, \(Q = 0\), so \(\Delta U = -W\), which means internal energy changes, so Statement I is incorrect. Statement II is correct since change in internal energy corresponds directly to the work done on or by the gas.

The change in temperature on the Celsius scale is equal to the change in temperature on the Kelvin scale because the size of one degree Celsius is equal to one Kelvin: \(\Delta T_{text{C}} = \Delta T_{\text{K}} = 2\text{ K}\).

According to the Zeroth Law of Thermodynamics, temperature is the physical quantity that determines if systems are in thermal equilibrium with each other.

Temperature is the physical quantity that determines thermal equilibrium. Two systems are in thermal equilibrium if and only if they are at the same temperature.

The mean free path is given by \(\lambda = \frac{1}{\sqrt{2} n \pi d^2}\). Since \(\lambda\) is inversely proportional to the number density \(n\), increasing the number density decreases the mean free path.

A rigid diatomic molecule has 3 translational and 2 rotational degrees of freedom, giving a total of 5 degrees of freedom.

Emissive power is defined as the thermal energy radiated per unit area per unit time. Its SI unit is \(\text{J m}^{-2}\text{s}^{-1}\) (or \(\text{W m}^{-2}\)).

Using the relation $\frac{T - \text{LFP}}{\text{UFP} - \text{LFP}} = \frac{C - 0}{100 - 0}$, we substitute $T = C$ for correct reading. This gives $\frac{C - 40}{80 - 40} = \frac{C}{100}$, which simplifies to $C = \frac{200}{3} ^\circ\text{C}$.