Two thin metallic spherical shells of radii r₁ and r₂ (r₁ < r₂) are placed with their centres coinciding. A material of thermal conductivity K is filled in the space between the shells. The inner shell is maintained at temperature $$\theta$$₁ and the outer shell at temperature $$\theta$$₂($$\theta$$₁ < $$\theta$$₂). The rate at which heat flows radially through the material is :-

A mixture of hydrogen and oxygen has volume 500 cm³, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

A reversible engine has an efficiency of $${1 \over 4}$$. If the temperature of the sink is reduced by 58$$^\circ$$C, its efficiency becomes double. Calculate the temperature of the sink :

For an ideal gas the instantaneous change in pressure 'p' with volume 'v' is given by the equation $${{dp} \over {dv}} = - ap$$. If p = p₀ at v =0 is the given boundary condition, then the maximum temperature one mole of gas can attain is : (Here R is the gas constant)