Question

Specific Heat

The heat capacity of an object indicates how much energy that object can absorb for a given increase in that object's temperature. In a system in which two objects of different temperatures come into contact with one another, the warmer object will cool and the cooler object will warm up until the system is at a single equilibrium temperature.

Note the difference between the terms molar heat capacity, which has units of J/(mol⋅∘C), and specific heat, which has units of J/(g⋅∘C).

In this problem answers are requested to three significant digits for grading purposes. The true number of significant digits may be more or less.

Part A

A volume of 120. mL of H2O is initially at room temperature (22.00 ∘C). A chilled steel rod at 2.00 ∘Cis placed in the water. If the final temperature of the system is 21.20  ∘C , what is the mass of the steel bar?

Use the following values:

specific heat of water = 4.18 J/(g⋅∘C)

specific heat of steel = 0.452 J/(g⋅∘C)

Express your answer to three significant figures and include the appropriate units.

mass of the steel =

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Part B

The specific heat of water is 4.18 J/(g⋅∘C). Calculate the molar heat capacity of water.

Express your answer to three significant figures and include the appropriate units.

molar heat capacity for water =

75.24Jmol°C

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Answer 1

A)

Density of water = 1.00 g/mL

Density = mass/volume

1.00 = mass/120

mass = 120 g

m₁C_p1T₁ = m₂C_p2T₂

where 1 represents water and 2 represents steel rod

120 4.18 (22.0 - 21.20) = m₂ 0.452 (21.20 - 2.00)

m₂ = 46.2 g

B)

Mol mass of water = 18 g/mol
18 g/mol x 4.18 J/g.°C = 75.24 J/mol.^oC (or K).