A rod CD of thermal resistance 10.0 KW^$$-$$1 is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 200$$^\circ$$C, 100$$^\circ$$C and 125$$^\circ$$C respectively. The heat current in CD is P watt. The value of P is ................. .

A system consists of two types of gas molecules A and B having same number density 2 $$\times$$ 10²⁵/m³. The diameter of A and B are 10 $$\mathop A\limits^o $$ and 5 $$\mathop A\limits^o $$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ____________ $$\times$$ 10^$$-$$2

The area of cross-section of a railway track is 0.01 m². The temperature variation is 10$$^\circ$$C. Coefficient of liner expansion of material of track is 10^$$-$$5/$$^\circ$$C. The energy stored per meter in the track is ____________ J/m.

(Young's modulus of material of track is 10¹¹ Nm^$$-$$2)

One mole of an ideal gas at 27$$^\circ$$ is taken from A to B as shown in the given PV indicator diagram. The work done by the system will be _________ $$\times$$ 10^$$-$$1 J. [Given : R = 8.3 J/mole K, ln2 = 0.6931] (Round off to the nearest integer)