Specific Heat Calculator
q = mcΔT, solved for heat, mass, specific heat capacity or temperature change.
Solve for
A difference, so °C and K are the same size. Negative means cooling.
Heat energy
4,184 J
4.184 kJ, absorbed by the substance.
Working
- q = mcΔT = 100 × 4.184 × 10 = 4184.00 J
What the equation says
Three things decide how much energy a temperature change takes: how much substance there is, what it is made of, and how big the change is. q = mcΔT is that sentence written down, and every calorimetry problem is a rearrangement of it.
Calorimetry in practice
In a coffee-cup calorimeter, the heat lost by a hot object equals the heat gained by the water, so the two mcΔT expressions are set equal and the unknown is solved for. That assumes nothing escapes to the room, which is why real measurements come out a little low.
Related: molar mass calculator, chemical equation balancer, periodic table.
How it works
Three things decide how much energy a temperature change takes: how much substance there is, what it is made of, and how big the change is. q = mcΔT is that sentence written down.
Specific heat / calorimetry
q = mcΔT m = q ÷ (cΔT) c = q ÷ (mΔT) ΔT = q ÷ (mc) ΔT = T_final − T_initial
- q
- heat energy, in joules. Negative means heat was released
- m
- mass, in grams
- c
- specific heat capacity, J/(g·°C). Water is 4.184
- ΔT
- temperature change — a difference, so °C and K are the same size
Heating 100 g of water by 10 °C
- m = 100 g
- c = 4.184 J/(g·°C)
- ΔT = 10 °C
- q = mcΔT
- q = 100 × 4.184 × 10
q = 4,184 J, or 4.184 kJ, absorbed by the water.
Good to know
- ΔT is a difference, so a change of 10 °C is a change of 10 K. Converting it to kelvin would be a mistake — only absolute temperatures need converting.
- Water's specific heat is unusually high, which is why the sea moderates coastal climates and why water is the standard coolant. It takes over four times the energy to warm a gram of water by a degree as a gram of aluminium.
- In a coffee-cup calorimeter the heat lost by the hot object equals the heat gained by the water, so the two mcΔT expressions are set equal. That assumes nothing escapes to the room, which is why real measurements come out a little low.
- A negative q means heat was released. Cooling gives a negative ΔT and so a negative q.
Related Calculators
Frequently Asked Questions
What is specific heat capacity?
The energy needed to raise one gram of a substance by one degree celsius. Water’s is unusually high at 4.184 J/(g·°C), which is why the sea moderates coastal climates and why water is the standard coolant.
What is the formula?
q = mcΔT: heat equals mass times specific heat capacity times temperature change. Rearranging it gives any of the four from the other three.
Does ΔT need converting to kelvin?
No — and converting it would be a mistake. ΔT is a difference, and a one-degree interval is the same size in celsius and kelvin, so a change of 10 °C is a change of 10 K. Only absolute temperatures need converting.
What does a negative answer mean?
That heat was released rather than absorbed. Cooling gives a negative ΔT and so a negative q, which is the convention: energy leaving the substance is negative.
Why does water heat up so slowly?
Because its hydrogen bonds absorb energy without the molecules speeding up much, and temperature measures how fast they move. It takes over four times as much energy to warm a gram of water by a degree as a gram of aluminium.