Question

Beryllium is a rare metal that is gray in color, strong, and lightweight. The following data was obtained from a calorimeter experiment:

5 sets of equations: m beryllium equals 10.1 grams. M water equals 38.8 grams. Delta T beryllium equals final T minus initial T equals 27.7 degrees Celsius minus 100 degrees Celsius. Delta T water equals Final T minus initial T equals 28.4 degrees Celsius minus 20.2 degrees Celsius. C water equals 4.18 joules per gram per degree Celsius.

The specific heat of beryllium is
J/g°C
C Subscript metal Baseline = StartFraction negative C Subscript water Baseline m Subscript water Baseline delta T Subscript water Over m Subscript metal Baseline delta T Subscript metal EndFraction. An irregular chunk of gray metal is shown.

Answer 1

Use energy conservation: q_metal + q_water = 0, so

C_metal = - (C_water m_water ΔT_water) / (m_metal ΔT_metal).

Plugging in the numbers (ΔT_metal = 27.7 − 100 = −72.3 °C, ΔT_water = 28.4 − 20.2 = 8.2 °C):

C_metal = −(4.18 J/g·°C × 38.8 g × 8.2 °C) / (10.1 g × (−72.3 °C))
= (1329.91 J) / (730.23 g·°C)
≈ 1.82 J/g·°C.

So the specific heat of the beryllium sample is about 1.82 J/g·°C.