Question

A 50.00 g sample of an unknown metal is heated to 45.00°C. It is then placed in a coffee-cup calorimeter filled with water. The calorimeter and the water have a combined mass of 250.0 g and an overall specific heat of 1.035 cal/g•°C. The initial temperature of the calorimeter is 10.00°C. The system reaches a final temperature of 11.08°C when the metal is added.

Which of the following equations is the correct one to use to calculate the specific heat of the metal?

C subscript p metal equals StartFraction m metal delta T metal over m calories C subscript p calorites delta T calories EndFraction.

C subscript p metal equals StartFraction negative m calories C subscript p calories delta T calories over m metal delta T metal EndFraction.

Answer 1

The second equation is correct:

Cp_metal = −(m_cal Cp_cal ΔT_cal) / (m_metal ΔT_metal).

Reason: energy conservation gives q_metal + q_cal = 0, so m_metal Cp_metal ΔT_metal + m_cal Cp_cal ΔT_cal = 0 and hence the negative sign is needed (ΔT_metal is negative, ΔT_cal positive).

(With the given numbers: ΔT_metal = 11.08 − 45.00 = −33.92°C, ΔT_cal = 11.08 − 10.00 = +1.08°C, so Cp_metal ≈ 0.165 cal/g·°C.)