# Thermal energy equation

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The thermal energy equation, Q = m c ΔT, establishes a relationship between the thermal energy (Q) of a substance and its mass (m), specific heat (c), and the temperature difference (ΔT). This equation enables the calculation of thermal energy by considering the mass of the substance, its specific heat, and the change in temperature.

Contents

## Practice problems

### Problem #1

Calculate the thermal energy required to raise the temperature of 1.5 kg of oil from 10 ℃ to 90 ℃, given that the specific heat of oil is 2.1 J/kg ℃.

Solution

Given data:

• Thermal energy, Q = ?
• Mass of oil, m = 1.5 kg
• Initial temperature of oil, Ti = 10 ℃
• Final temperature of oil, Tf = 90 ℃
• Therefore, the temperature difference, ΔT = Tf – Ti = 80 ℃
• Specific heat of oil, c = 2.1 J/kg ℃

Applying the formula:

• Q = m c ΔT
• 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 g of a substance is heated, its temperature increases from 20 ℃ to 70 ℃. Calculate the thermal energy required to raise the temperature of the substance, considering its specific heat of 4.8 J/kg ℃.

Solution

Given data:

• Mass of a substance, m = 500 g = 0.5 kg
• Initial temperature, Ti = 20 ℃
• Final temperature, Tf = 70 ℃
• Therefore, the temperature difference, ΔT = Tf – Ti = 50 ℃
• Specific heat, c = 4.8 J/kg ℃
• Thermal energy, Q = ?

Applying the formula:

• Q = m c ΔT
• Q = 0.5 × 4.8 × 50
• Q = 120 J

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

### Problem #3

A 750 g sample of a material is heated, causing its temperature to increase from 35 ℃ to 85 ℃. Calculate the amount of thermal energy required to raise the temperature of the material, given that its specific heat is 1.6 J/kg ℃.

Solution

Given data:

• Mass of a material, m = 750 g = 0.75 kg
• Initial temperature, Ti = 35 ℃
• Final temperature, Tf = 85 ℃
• Therefore, the temperature difference, ΔT = Tf – Ti = 50 ℃
• Thermal energy, Q = ?
• Specific heat, c = 1.6 J/kg ℃

Applying the formula:

• Q = m c ΔT
• Q = 0.75 × 1.6 × 50
• Q = 60 J

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

### Problem #4

Calculate the thermal energy needed to raise the temperature of a 2 kg wooden object from 24 ℃ to 64 ℃. The specific heat of wood is 3.4 J/kg ℃.

Solution

Given data:

• Thermal energy, Q = ?
• Mass of a wooden object, m = 2 kg
• Initial temperature, Ti = 24 ℃
• Final temperature, Tf = 64 ℃
• Therefore, the temperature difference, ΔT = Tf – Ti = 40 ℃
• Specific heat, c = 3.4 J/kg ℃

Applying the formula:

• Q = m c ΔT
• Q = 2 × 3.4 × 40
• Q = 272 J

Therefore, the thermal energy required to raise the temperature of a wooden object is 272 J.