The specific heat capacity of a substance is the amount of heat required to raise the temperature of 1 kilogram of the substance by 1 Kelvin (or 1°C). It is a fundamental concept in thermodynamics and is symbolized by c.
The heat energy Q required to raise the temperature of a mass m by a temperature change ΔT is given by:
\[ Q = mc\Delta T \]
Specific heat capacity is measured in J·kg⁻¹·K⁻¹ (joules per kilogram per kelvin).
Problem: How much energy is required to heat 0.5 kg of water from 20°C to 70°C? (Specific heat capacity of water = 4200 J·kg⁻¹·K⁻¹)
Solution:
Given:
Using the formula:
\[ Q = mc\Delta T = 0.5 \times 4200 \times 50 = 105000 \text{ J} \]
Answer: 105,000 J (or 105 kJ)
Problem: A 2 kg aluminum block cools from 100°C to 30°C. How much heat energy is released? (Specific heat capacity of aluminum = 900 J·kg⁻¹·K⁻¹)
Solution:
\[ Q = mc\Delta T = 2 \times 900 \times 70 = 126000 \text{ J} \]
Answer: 126,000 J (or 126 kJ)
Problem: A 0.4 kg metal takes 3200 J of heat to raise its temperature from 25°C to 45°C. Find the specific heat capacity of the metal.
Solution:
Rearranging the formula:
\[ c = \frac{Q}{m\Delta T} = \frac{3200}{0.4 \times 20} = \frac{3200}{8} = 400 \, \text{J·kg}^{-1}\text{·K}^{-1} \]
Answer: 400 J·kg⁻¹·K⁻¹
Written by Thenura Dilruk