Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity K₁ , K₂ and K₃ , respecrtively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100^oC and the other at 0^oC (see figure). If the joints of the rod are at 70^oC and 20^oC in steady state and there is no loss of energy from the surface of the rod, the correct relationship between K₁ , K₂ and K₃ is :

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 :