Thermal Energy Equation | Problems (And Solutions)

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.

.
.
.

Related:

Also Read:

Leave a Comment