Physics

Physics

Problem

A laboratory technician wishes to determine the specific heat capacity of a newly synthesized solid compound. The technician heats 8.50 g of the compound from 18.4 °C to 95.6 °C using an electric heater that delivers energy at a constant rate of 42.0 W. The heating takes exactly 155 s. (a) Determine the total quantity of heat (in joules) delivered to the compound during the heating interval. (b) Using the result from part (a), calculate the specific heat capacity of the compound in J g−1 ∘C−1\text{J}\,\text{g}^{-1}\,{}^{\circ}\text{C}^{-1}, reporting your answer with the correct number of significant figures. (c) Circle the statement that correctly describes how the calculated specific heat capacity would change, if at all, had the heater operated for the same total time but at 21.0 W instead of 42.0 W. Justify your selection with appropriate reasoning. • It would be larger • It would be smaller • It would be unchanged
Intuitive explanation

The key is recognizing that all the electrical energy delivered by the heater goes into raising the temperature of the solid—so you can find the total energy input, then use the heat capacity equation q=mcΔTq = mc\Delta T to solve for the unknown specific heat cc. Start by calculating the total joules supplied (power × time), then rearrange the equation to isolate cc using the measured mass, temperature change, and energy absorbed.

Intuitive explanation

The key is recognizing that all the electrical energy delivered by the heater goes into raising the temperature of the solid—so you can find the total energy input, then use the heat capacity equation q=mcΔTq = mc\Delta T to solve for the unknown specific heat cc. Start by calculating the total joules supplied (power × time), then rearrange the equation to isolate cc using the measured mass, temperature change, and energy absorbed.

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