**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, T_{i} = 10 °C

Final temperature of oil, T_{f} = 90 °C

Temperature difference, ΔT = T_{f} – T_{i} = 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, T_{i} = 20 °C

Final temperature of water, T_{f} = 70 °C

Temperature difference, ΔT = T_{f} – T_{i} = 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, T_{i} = 35 °C

Final temperature of aluminium, T_{f} = 85 °C

Temperature difference, ΔT = T_{f} – T_{i} = 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, T_{i} = 24 °C

Final temperature of wood, T_{f} = 64 °C

Temperature difference, ΔT = T_{f} – T_{i} = 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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**Related:**

- Potential Energy Formula
- Gravitational Potential Energy Formula
- Electric Potential Energy Formula
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- Kinetic Energy Formula
- Rotational Kinetic Energy Formula
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