A solid copper sphere of radius 4.0 cm is removed from a furnace and immediately…
PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter
Problem
A solid copper sphere of radius 4.0 cm is removed from a furnace and immediately placed on an insulating stand in a laboratory whose ambient temperature is approximately constant at 300 K. Assume the sphere’s surface temperature is uniform at every instant and that no energy is lost by any mechanism other than electromagnetic emission.
During the first 600 s after removal, laboratory instruments continuously record the radiant power leaving the sphere’s surface. A student later examines the record and produces a smooth, monotonically decreasing power-versus-time graph.
(a) Describe qualitatively how the shape of the power-versus-time graph is related to the way the sphere cools. In your description, explicitly address why the graph does not follow a straight line and what features of the physical situation control its curvature.
(b) Explain how the student could use the power-versus-time graph to determine the total thermal energy emitted by the sphere during the 600 s interval. In your explanation, identify the physical meaning of the relevant area or geometric feature on the graph and discuss unit consistency.
(c) Suppose a second identical sphere is removed from the furnace at twice the temperature of the first sphere. Without performing a detailed calculation, predict and justify how the entire power-versus-time curve for this hotter sphere would compare with that of the first sphere during the first few seconds after removal.