Chapter 3 · Matter and Energy
3.12Energy and Heat Capacity Calculations
12 min · two checks
Predict
How much energy does it take to warm 200 g of water by 10 °C?
The idea
- Solve q = m c ΔT for heat, mass, or ΔT.
- Track the sign: heating the system means positive q.
Substitute carefully. Mass in grams, specific heat in J/(g·°C), and ΔT in °C produce joules. ΔT is final minus initial if q is heat absorbed by the sample. Warming water from 20.0 °C to 35.0 °C is ΔT = 15.0 °C, not 35. If you are asked how much the sample releases as it cools, compute the positive energy from the size of ΔT and then describe the direction in words, or report q as negative for the sample.
Units cancel to joules only if c’s units match the mass unit. Mixing kilograms with a per-gram specific heat is a factor-of-1000 error. Significant figures follow the measurements; 4.184 has four figures but will not rescue a ΔT known only to two. For two objects in contact that reach the same final temperature, the heat lost by one equals the heat gained by the other if the container is ignored. That sets up m₁ c₁ ΔT₁ + m₂ c₂ ΔT₂ = 0.
Keep these
- q = m c ΔT, with ΔT = Tfinal − Tinitial for heat absorbed.
- Match the mass unit to the specific-heat unit.
- Heat lost by a hot object equals heat gained by a cold one in an ideal contact problem.
Worked path
How much heat, in kJ, is absorbed when 250. g of water warms from 21.0 °C to 86.0 °C?
Observe
m = 250. g, c = 4.184 J/(g·°C), ΔT = 65.0 °C.