Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom.The gas is maintained at a temperature of T. The total internal energy, U of a mole of this gas, and the value of
$$\gamma \left( { = {{{C_p}} \over {{C_v}}}} \right)$$ are given, respectively by:

Two different wires having lengths L₁ and L₂, and respective temperature coefficient of linear expansion $$\alpha $$₁ and $$\alpha $$₂, are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is :

A bullet of mass 5 g, travelling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is 0.030 cal/(g – ^oC) (1 cal = 4.2 × 10⁷ ergs) close to :