Physics Lesson 13.4.2 - What is a Calorimeter?

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Welcome to our Physics lesson on What is a Calorimeter?, this is the second lesson of our suite of physics lessons covering the topic of Calorimetry (Heat Transfer), you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

What is a Calorimeter?

A calorimeter is an insulated container used to measure the specific heat capacity of an unknown solid by means of heat exchange approach. The only difference with the previous examples lies in the fact that the materials do not mix to obtain a homogenous mixture but they remain two distinct materials even after the thermal equilibrium is established (when both materials reach the same temperature). The rest is the same.

Example 4

A 20 g metal piece at 120°C is inserted into a calorimeter, which contains 200 g of water at 20°C. When thermal equilibrium is established, the final temperature of metal becomes 22°C. What is the specific heat capacity of metal if water has a specific heat capacity of 1 cal/g°C?

Solution 4

From the equation of heat exchange

Q_{released by the hot object} = Q_{gained by the cold object}

we can determine the value of specific heat capacity of metal, given that

m₁ = 20 g
t₁ = 120°C
m₂ = 200 g
t₂ = 20°C
t_mix = 22°C
c₁ = 1 cal/g°C
c₂ = ?

Thus, substituting the above values in the equation

m₁ × c₁ × (t₁ - t_f ) = m₂ × c₂ × (t_f - t₂ )

we obtain

20 × c₁ × (120 - 22) = 200 × 1 × (22 - 20)
20 × c₁ × 98 = 200 × 2
1960 × c₁ = 400
c₁ = 400/1960
=0.204 cal/g°C

We can use the heat exchange method described above to calculate the final temperature even when one of the substances experiences any change in phase during the process. Let's consider an example.

Example 5

A 20 g ice cube at -5°C is inserted into a container, in which there are 100 g of water at 60°C. What will be the final temperature of the system after the thermal equilibrium is established? Take c_ice = 0.5 cal/g°C, c_water = 1 cal/g°C and L_ice = 80 cal/g.

Solution 5

Most likely (given the difference in mass), the ice cube will experience three stages: 1- increase in temperature up to the melting point (for water it is 0°C), 2- melting process (without any change in temperature) and 3- increase in temperature of water up to the final temperature.

The general equation in the specific case is

m_ice × c_ice × ∆t_ice+m_ice × L_ice+m_{former ice(now cold water)} × c_water × ∆t_{cold water}=m_{hot water} × c_ice × ∆t_ice

Substituting the values, we obtain

20 × 0.5 × [0 - (-5)]+20 × 80+20 × 1 × (t_f - 0) = 100 × 1 × (60 - t_f)
50 + 1600 + 20 × t_f = 6000 - 100 × t_f
20 × t_f + 100 × t_f = 6000 - 1600
120 × t_f = 4400
t_f = 36.7°C

You have reached the end of Physics lesson 13.4.2 What is a Calorimeter?. There are 3 lessons in this physics tutorial covering Calorimetry (Heat Transfer), you can access all the lessons from this tutorial below.

More Calorimetry (Heat Transfer) Lessons and Learning Resources

Thermodynamics Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
13.4	Calorimetry (Heat Transfer)
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
13.4.1	Heat Transfer
13.4.2	What is a Calorimeter?
13.4.3	Methods of Heat Transfer

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