Specific Heat Capacity
Why iron heats up nine times faster than water, and how to measure it.
Lesson at a glanceShow the key points
- Q = msΔθ (25.1); s in J kg⁻¹ K⁻¹ or cal g⁻¹ °C⁻¹. Water 4186, aluminium 900, iron 470, copper 389, lead 130.
- Molar heat capacity C: Q = nCΔθ. Heat capacity = ms; water equivalent = mass of water of equal heat capacity.
- Regnault: heat a solid in a steam chamber, drop into a calorimeter: m₁s₁(θ₁ − θ) = (m₂s₂ + m₃s₃)(θ − θ₂).
- Same apparatus with a known solid gives a liquid's specific heat.
Heat a kilogram of water and a kilogram of iron with the same burner and the iron gets hot nine times faster. Each material has its own appetite for heat.
Specific heat capacity
The heat needed to change a body’s temperature depends on its mass, the temperature change, its material and conditions such as pressure:
| Material | cal g⁻¹ °C⁻¹ | J kg⁻¹ K⁻¹ |
|---|---|---|
| Water | 1.00 | 4186 |
| Ice | 0.50 | 2093 |
| Steam | 0.46 | 1926 |
| Aluminium | 0.215 | 900 |
| Iron | 0.112 | 470 |
| Copper | 0.093 | 389 |
| Mercury | 0.033 | 138 |
| Lead | 0.031 | 130 |
(Values at constant pressure, as for solids and liquids heated in the open air.)
How much heat raises an 80 g aluminium block by 25°C? (s = 0.215 cal g⁻¹ °C⁻¹.)
Molar heat capacity, heat capacity and water equivalent
- Counting the amount in moles instead: Q = nCΔθ, where C is the molar heat capacity.
- The product ms is the body’s heat capacity (J/K).
Measuring specific heat: Regnault’s method
For a solid denser than water and insoluble in it. The solid hangs in a double-walled steam chamber until its temperature (θ₁) is steady. A calorimeter of water at θ₂ is slid under it, the solid dropped in, and the highest temperature θ reached is noted. Heat lost by the solid = heat gained by calorimeter and water:
The same apparatus finds a liquid’s specific heat: use a solid of known s₁ and the liquid in place of water, then solve for s₃.
copper calorimeter, 50 g
A 100 g metal ball at 100°C is dropped into 150 g of water at 20.0°C in a 50 g copper calorimeter. The mixture settles at 25.4°C. Find the metal’s specific heat (in cal g⁻¹ °C⁻¹).
- 1Q = msΔθ; s is specific heat capacity. Q = nCΔθ with molar heat capacity C.
- 2Heat capacity = ms; water equivalent = mass of water with the same heat capacity.
- 3Regnault's method: m₁s₁(θ₁ − θ) = (m₂s₂ + m₃s₃)(θ − θ₂).
Check yourself
Keep exploring
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