NEET Thermal Physics MCQs & PYQs

The average translational kinetic energy per molecule of any gas is given by \(\frac{3}{2} k_B T\). Since both gases are at the same temperature, the ratio of their translational kinetic energies is 1 : 1.

Metal is a much better conductor of heat than wood. When touched in winters, heat is rapidly conducted away from our hand to the metal surface, making it feel colder.

The internal energy of an ideal gas is a function of temperature only, as there are no intermolecular forces of attraction in an ideal gas. Therefore, \( U \propto T \).

For an isothermal process, the change in internal energy is \( \Delta U = 0 \). According to the first law of thermodynamics, \( Q = \Delta U + W \), which gives \( Q = 0 + 150\text{ J} = 150\text{ J} \).

Each vibrational mode has both kinetic energy and potential energy modes, thus having two degrees of freedom. Therefore, the average energy per vibrational mode is \(2 \times \frac{1}{2} k_B T = k_B T\).

Coefficient of volume expansion is three times the coefficient of linear expansion for an isotropic solid, i.e., \(\gamma = 3\alpha\).

At STP, 1 mole of an ideal gas occupies $22.4 \text{ L}$. The number of moles in $4.5 \text{ kg}$ of water is $n = \frac{4500 \text{ g}}{18 \text{ g/mol}} = 250 \text{ moles}$. The volume is $V = 250 \times 22.4 \text{ L} = 5600 \text{ L} = 5.6 \text{ m}^3$.

Using the ideal gas law in terms of density, $P = \frac{\rho RT}{M}$, we get $\rho = \frac{PM}{RT}$. For hydrogen, $M = 2 \times 10^{-3} \text{ kg/mol}$. Thus, $\rho = \frac{249 \times 10^3 \times 2 \times 10^{-3}}{8.3 \times 300} = 0.2 \text{ kg/m}^3$.

In the equation $P = \frac{\rho RT}{M_0}$, $\rho$ represents the mass density (mass per unit volume) of the gas, and $M_0$ is the molar mass of the gas.

According to the kinetic theory of gases, the average kinetic energy of gas molecules is directly proportional to its absolute temperature ($E_k \propto T$). Therefore, an increase in temperature increases its kinetic energy.