Two metallic blocks M₁ and M₂ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M₂ is K then the thermal conductivity of M₁ will be :

[Assume steady state heat conduction]

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 :