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), andspecific 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

Q = m c ∆T
Q = quantity of heat in joules (J)
m = mass of the substance acting as the environment in
grams (g)
c = specific heat capacity (4.19 for H2O) in J/(g ^oC)
∆T = change in temperature = Tfinal - Tinitial in ^oC

Part A

120 x (22-21.2) x 4.18 = mass x 0.452 x (22-2)

Mass = 401.28 / 9.04 = 44.389

Mass of the steel bar = 44.389 gm

Part B

we know 4.18 joules per gram to raise one degree C

Next. We find out how many moles of water are in 1 gram

1 mole of water is 18 grams (oxygen weighs 16 gram/mole, hydrogen weighs 1 gram/mole) , so 1 gram is 1/18 mole

4.18 x 18= 75.24 joules required to raise 1 mole 1 degree C

molar heat capacity 75.24 J/molC