Thermal Energy Equation | Problems (And Solutions)

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Thermal Energy Equation

Thermal energy or heat energy (Q) is the product of mass (m), specific heat (c) and the temperature difference (ΔT). Using the equation of thermal energy: Q = m c ΔT, the value of thermal energy of a substance can be calculated.

Let’s solve some problems based on this equation, so you’ll get a clear idea.

Thermal Energy Practice Problems

Problem 1: Calculate the thermal energy required to raise the temperature of 1.5 kg of oil from 10 °C to 90 °C. The specific heat of oil is 2.1 J/kg °C.

Solution:

Given data:
Thermal energy, Q = ?
Mass of oil, m = 1.5 kg
Initial temperature of oil, Ti = 10 °C
Final temperature of oil, Tf = 90 °C
Temperature difference, ΔT = Tf – Ti = 80 °C
Specific heat of oil, c = 2.1 J/kg °C

Using the equation of thermal energy,
Q = m c ΔT
Q = 1.5 × 2.1 × (90 – 10)
Q = 1.5 × 2.1 × 80
Q = 252 J

Therefore, the thermal energy required to raise the temperature of oil is 252 J.

Problem 2: When 500 gm of water is heated, the temperature of water increases from 20 °C to 70 °C. If the specific heat of water is 4.8 J/kg °C, then what thermal energy is required to raise the temperature of water?

Solution:

Given data:
Mass of water, m = 500 gm = 0.5 kg
Initial temperature of water, Ti = 20 °C
Final temperature of water, Tf = 70 °C
Temperature difference, ΔT = Tf – Ti = 50 °C
Specific heat of water, c = 4.8 J/kg °C
Thermal energy, Q = ?

Using the equation of thermal energy,
Q = m c ΔT
Q = 0.5 × 4.8 × (70 – 20)
Q = 0.5 × 4.8 × 50
Q = 120 J

Therefore, the thermal energy required to raise the temperature of water is 120 J.

Problem 3: A 750 gm of aluminium is heated and its temperature is raised from 35 °C to 85 °C. Calculate the thermal energy required to raise the temperature of aluminium. The specific heat of aluminium is 1.6 J/kg °C.

Solution:

Given data:
Mass of aluminium, m = 750 gm = 0.75 kg
Initial temperature of aluminium, Ti = 35 °C
Final temperature of aluminium, Tf = 85 °C
Temperature difference, ΔT = Tf – Ti = 50 °C
Thermal energy, Q = ?
Specific heat of aluminium, c = 1.6 J/kg °C

Using the equation of thermal energy,
Q = m c ΔT
Q = 0.75 × 1.6 × (85 – 35)
Q = 0.75 × 1.6 × 50
Q = 60 J

Therefore, the thermal energy required to raise the temperature of aluminium is 60 J.

Problem 4: What thermal energy is required to raise the temperature of a 2 kg wood from 24 °C to 64 °C? The specific heat of a wood is 3.4 J/kg °C.

Solution:

Given data:
Thermal energy, Q = ?
Mass of wood, m = 2 kg
Initial temperature of wood, Ti = 24 °C
Final temperature of wood, Tf = 64 °C
Temperature difference, ΔT = Tf – Ti = 40 °C
Specific heat of wood, c = 3.4 J/kg °C

Using the equation of thermal energy,
Q = m c ΔT
Q = 2 × 3.4 × (64 – 24)
Q = 2 × 3.4 × 40
Q = 272 J

Therefore, the thermal energy required to raise the temperature of wood is 272 J.

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