A 18 g sample of metal is heated to 96°C and placed in a calorimeter containing 21 g of water at an initial temperature of 24°C. After the metal cools in the water bath, the final temperature inside the calorimeter is 26°C. What is the (positive) specific heat of the metal rounded to the HUNDREDTHS place? (hint: final temperatures of metal and water are the same). Do NOT include units. *

140

Explanation:

Given the following :

Mass of metal = 18g = 0.018kg

Mass of water (calorimeter) = 21g = 0.021kg

Initial temperature of metal = 273 + 96 = 369k

Initial temperature of water = 273 + 24 = 297k

Final temperature inside calorimeter = 273 + 26 = 299k

Temperature change of metal = 299 - 369= -70k

Temperature change of water = 299 - 297 = 2k

H = mc ΔT

m = mass

c = specific heat capacity

ΔT = change in temperature

Heat lost by metal = heat gained by water

mc ΔT = mc ΔT

Specific heat capacity of water = 4200

18 * C * ( 299 - 369 ) = 21 * 4.2 * ( 299 - 297)

0.018 × C × -70 = 0.021 × 4.2 × 2

- 1.26 × C = 0.1764

C = 176.4/1.26

C = 140

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