A student has of water at in an insulated container

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A student has

0.500\,\text{kg}

of water at

80^{\circ}\text{C}

in an insulated container. The student wishes to lower the water’s temperature to

40^{\circ}\text{C}

by adding identical solid copper spheres, each of mass

0.050\,\text{kg}

and initial temperature

5^{\circ}\text{C}

. The specific heat of copper is

385\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}

, and the specific heat of water is

4.18\times10^{3}\,\text{J}\,\text{kg}^{-1}\,\text{K}^{-1}

. Neglect any energy absorbed by the container itself and assume no energy is exchanged with the surroundings. (1) Determine the minimum number of copper spheres the student must add so that the final temperature of the mixture is

40^{\circ}\text{C}

or lower. Show all algebraic steps and clearly state any assumptions you make. (2) Explain why adding fewer spheres than the number you calculated would not be sufficient to reach the desired temperature.

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