PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
Three identical blocks X, Y, and Z, each of mass m and specific heat capacity c, are arranged in a straight line on a thermally insulating tabletop. The initial temperatures of the blocks are:
X: 450KY: 300KZ: 250K.
Blocks X and Y are in direct thermal contact. Block Y touches Z through a thin insulating sheet that reduces the rate of energy transfer across that interface to one-half of what it would be for direct contact between identical surfaces. The entire three-block system is thermally isolated from the surroundings.
Neglect any energy exchange with the air.
(a) Immediately after the blocks are placed as described, indicate the direction of net energy transfer (if any) between each adjacent pair of blocks (X\,→\,Y, Y\,→\,Z, or no net transfer). Justify your answers qualitatively using temperature considerations.
(b) Show, using an energy-conservation argument, that the final equilibrium temperature Tf of the three-block system is independent of the presence or absence of the insulating sheet between Y and Z.
(c) Derive an algebraic expression for Tf in terms of the given quantities m, c, and the initial temperatures of the three blocks.
(d) Compare qualitatively the time required to reach equilibrium in the actual arrangement (with the insulating sheet) to the time that would be required if all three blocks were in perfect direct contact. Explain your reasoning without using any detailed heat-transfer equations.