By Lee Johnson
Updated Aug 30, 2022

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TL;DR

Use the formula Q = mcΔT to calculate heat absorbed.

• Q = heat absorbed (J)
• m = mass of the substance (kg)
• c = specific heat capacity (J kg⁻¹ °C⁻¹)
• ΔT = change in temperature (°C)

Thermodynamic Foundations

The first law of thermodynamics states that the change in internal energy of a system equals the heat added to it plus the work done on it. Heat is a form of energy transfer that occurs only between bodies at different temperatures; it flows spontaneously from hot to cold. Understanding these principles is essential for accurate heat calculations.

Specific Heat Capacity

Specific heat capacity, denoted c, quantifies how much energy is required to raise the temperature of 1 kg of a material by 1 °C. Typical values include:

• Water: 4 181 J kg⁻¹ °C⁻¹
• Lead: 128 J kg⁻¹ °C⁻¹

A higher c means the material requires more energy to change temperature.

Calculating Heat Absorption

Apply the simple relation Q = mcΔT. First determine the temperature change: ΔT = T_final – T_initial.

Example: Raise 2 kg of water from 10 °C to 50 °C.

• ΔT = 50 °C – 10 °C = 40 °C
• Q = 2 kg × 4 181 J kg⁻¹ °C⁻¹ × 40 °C = 334 480 J (≈334.5 kJ)

Thus, approximately 334.5 kJ of heat is required.

Unit Consistency and Conversion

Specific heat capacities may appear in alternative units: joules per gram per °C, calories per gram per °C, or joules per mole per °C. Keep units consistent throughout the calculation. For example, if c is given in J g⁻¹ °C⁻¹, use mass in grams; if it’s in J mol⁻¹ °C⁻¹, express mass in moles. Temperature differences measured in Kelvin are numerically identical to Celsius differences, so ΔT can be used directly.

When converting between energy units, remember: 1 calorie = 4.184 J.