Section 7.3: Heat Capacity and Specific Heat Capacity
Heat capacity and specific heat capacity describe how substances store thermal energy when heated.
Heat Capacity (C): Amount of heat needed to raise the temperature of an object by 1 K (or 1 °C).
\[
C = \frac{Q}{\Delta T}
\]
where \( Q \) = heat absorbed (J), \( \Delta T \) = temperature change (K or °C)
Specific Heat Capacity (c): Heat capacity per unit mass.
\[
c = \frac{Q}{m \Delta T}
\]
where \( m \) = mass (kg), \( Q \) = heat absorbed (J), \( \Delta T \) = temperature change
Relationship between heat, mass, and temperature change:
\[
Q = m c \Delta T
\]
Example 1: Heating a Metal
A 2 kg block of aluminum (\( c = 900 \, \text{J/kg·K} \)) is heated from 20 °C to 80 °C. Find the heat absorbed.
\[
Q = m c \Delta T = 2 \cdot 900 \cdot (80-20) = 108{,}000 \text{ J}
\]
The block absorbs 108,000 J of heat.
Example 2: Calculating Specific Heat
A 5 kg object absorbs 20,000 J of heat and its temperature rises by 10 K. Find its specific heat capacity.
\[
c = \frac{Q}{m \Delta T} = \frac{20{,}000}{5 \cdot 10} = 400 \, \text{J/kg·K}
\]
The specific heat capacity is 400 J/kg·K.
Practice Problems
- A 3 kg block of iron (\( c = 450 \, \text{J/kg·K} \)) is heated from 25 °C to 75 °C. Calculate the heat absorbed.
- A 4 kg object absorbs 36,000 J and its temperature rises by 12 K. Find its specific heat capacity.
- A 0.5 kg cup of water (\( c = 4180 \, \text{J/kg·K} \)) is heated by 15 K. How much heat is required?
- How much heat is required to raise the temperature of 1.2 kg of copper (\( c = 385 \, \text{J/kg·K} \)) from 20 °C to 100 °C?
- An unknown material of mass 2 kg absorbs 25,000 J and increases in temperature by 20 K. Find its specific heat capacity.
- A 6 kg metal block is cooled from 100 °C to 40 °C. How much heat does it lose if \( c = 500 \, \text{J/kg·K} \)?
- Explain the difference between heat capacity and specific heat capacity.
- A 0.8 kg copper wire is heated from 30 °C to 60 °C. Calculate the heat absorbed.
- Calculate the specific heat of a 10 kg object that absorbs 50,000 J to rise 25 K.
- Why is water’s high specific heat capacity important for climate regulation?