Two metal spheres

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

Two

100.0\,\text{g}

metal spheres, one made of copper and the other of lead, are removed from a water bath maintained at

100.0\,^\circ\text{C}

and immediately placed on identical, perfectly insulating platforms exposed to still air at

22.0\,^\circ\text{C}

. During the first

1.00\,\text{kJ}

of energy loss, each sphere loses exactly the same quantity of energy to the surroundings. The specific heat capacities are

0.385\,\mathrm{J\,g^{-1}\,^{\circ}C^{-1}}

for copper and

0.129\,\mathrm{J\,g^{-1}\,^{\circ}C^{-1}}

for lead. (a) Derive an expression that relates the temperature change

\Delta T

of a solid object to its mass

m

, specific heat capacity

c

, and the quantity of energy

q

lost or gained. (b) Using your expression, calculate the temperature of each sphere after it has lost

1.00\,\text{kJ}

of energy. (c) If the spheres were allowed to continue cooling under the same conditions, which one would reach

22.0\,^\circ\text{C}

first? Support your answer with quantitative reasoning based on the data provided.