# A-level Physics (Advancing Physics)/Specific Heat Capacity

It takes energy to heat things up, since heat is work. If we heat a more massive thing up, it takes more work, because we have to give more particles, on average, an energy kT. Some substances require more work to heat up than others. This property is known as specific heat capacity. This gives us the formula:

$\Delta E=mc\Delta \theta$ ,

where ΔE is the work put in to heating something up (in J), m is the mass of the thing we are heating up (in kg), c is the specific heat capacity (in Jkg−1K−1), and Δθ is the difference in temperature due to the work done on the substance (in degrees Celsius or Kelvin). Note that some textbooks may replace ∆E with Q or q, and ∆θ with ∆T, however they represent the same concepts.

It should be noted that the specific heat capacity changes slightly with temperature, and more than slightly when the material changes state. A table of the specific heat capacities of various substances is given below:

Substance State Temperature (°C) Specific Heat Capacity (kJkg−1K−1)
Air gas 23 1.01
Aluminium solid 25 0.90
Animal (and human) tissue mixed 25 3.5
Argon gas 25 0.52
Copper solid 25 0.39
Glass solid 25 0.84
Helium gas 25 5.19
Hydrogen gas 25 14.3
Iron solid 25 0.45
Nitrogen gas 25 1.04
Oxygen gas 25 0.92
Uranium solid 25 0.12
Water solid -10 2.05
Water liquid 25 4.18
Water gas 100 2.08

## Questions

1. How much work would it take to heat 100 kg of liquid water from 20 °C to 36.8 °C?

2. How much work would it take to heat a well-insulated room from 15 °C to 21 °C, if the room is a cube with side length 10m, and the density of the air is 1.2kgm−3?

3. A 10 kg block of iron at 80 °C is placed in the room above once it has reached 21 °C. If the iron cools by 40 °C, what is the new temperature of the room?