Formula of Heat: Q = mcΔT, Latent Heat and H = I²Rt

The formula of heat for warming or cooling a substance is $Q = mc\Delta T$ : multiply the mass m by the specific heat capacity c and the temperature change ΔT. It gives the energy, in joules, that must flow in or out to change the temperature without changing the state.

Two more heat formulas come up in school physics. When a substance melts or boils at constant temperature, use $Q = mL$ with the latent heat L. In the Class 10 electricity chapter, the heat produced in a resistor is $H = I^2Rt$ . This page covers all three, since each is what students mean by the heat formula in physics at some stage.

Quick facts

Temperature change
$Q = mc\Delta T$
Change of state
$Q = mL$
Electrical heating
$H = I^2Rt$
SI unit
joule (J); 1 cal = 4.186 J
Dimensions
[M¹ L² T⁻²], the same as energy
Water
c ≈ 4186 J/(kg K), often rounded to 4200

Symbols in the formula of heat used in physics

Parts of Q = mcΔT
Symbol	Meaning	SI unit
$Q$	Heat gained (positive) or lost (negative)	J
$m$	Mass	kg
$c$	Specific heat capacity of the material	J/(kg K)
$\Delta T$	Final temperature minus initial	K, same size as °C

A change of 1 K equals a change of 1 °C, so ΔT needs no conversion between the two scales. Water has a high c, which is why it warms slowly and is used in radiators and car cooling systems. Metals such as copper (about 385 J/(kg K)) and aluminium (about 900 J/(kg K)) heat up far faster.

Solved examples

Example 1: heating water

How much heat raises 2.0 kg of water from 20 °C to 70 °C? Take c = 4186 J/(kg K).

$Q = (2.0)(4186)(50) = 4.19\times10^{5}\ \text{J}$

That is about 419 kJ.

Example 2: mass in grams

A 250 g aluminium block is heated from 25 °C to 125 °C. Take c = 900 J/(kg K).

m = 0.250 kg, ΔT = 100 K.

$Q = (0.250)(900)(100) = 2.25\times10^{4}\ \text{J}$

Example 3: melting ice

Find the heat to melt 0.50 kg of ice at 0 °C. Latent heat of fusion is 3.34 × 10⁵ J/kg.

$Q = mL = (0.50)(3.34\times10^{5}) = 1.67\times10^{5}\ \text{J}$

The temperature stays at 0 °C until all the ice has melted.

Heat formula physics class 10: heating effect of current

In the electricity chapter, the heat produced when current I flows through resistance R for time t is Joule's law of heating:

$H = I^2Rt = VIt = \frac{V^2}{R}t$

Example 4: an electric iron element

A current of 2.0 A flows through a 50 Ω element for 1 minute. Find the heat produced.

$H = (2.0)^2(50)(60) = 1.2\times10^{4}\ \text{J}$

This links heat to the resistance and current formulas. Fuses and heaters rely on it.

Heat balance in mixtures

When a hot object and a cold one are mixed in an insulated container, heat lost by the hot one equals heat gained by the cold one:

$m_1c_1(T_1 - T_f) = m_2c_2(T_f - T_2)$

Solve for the final temperature $T_f$ . If ice is involved, add an $mL$ term for melting. This is the principle of calorimetry, and it is just conservation of energy, the idea behind the first law of thermodynamics.

Heat is energy in transit because of a temperature difference. Temperature is how hot something is. A bath holds more heat energy than a cup of boiling water, at a lower temperature.

Units and conversions

Heat units you may see
Unit	Value in joules
1 calorie (cal)	4.186 J
1 kilocalorie (food Calorie)	4186 J
1 kJ	1000 J
1 kW h	3.6 × 10⁶ J

Heat is an energy, so it shares the dimensions [M¹ L² T⁻²] with work, as shown on the dimensional formula of energy page.

Slips to avoid

Leaving mass in grams when c is in J/(kg K).
Using Q = mcΔT during melting or boiling, where ΔT is zero.
Getting the sign of ΔT wrong when the body cools.
Forgetting to square the current in H = I²Rt.

The thermodynamics formula sheet lists every related topic, and Newton's law of cooling shows how fast a hot object loses heat.

Frequently asked questions

What is the formula of heat in physics?

Q = mcΔT for a temperature change, and Q = mL for a change of state at constant temperature.

What is the heat formula in physics class 10?

In the electricity chapter it is H = I²Rt, the heat produced by a current I in a resistance R in time t.

Which unit is heat measured in?

The joule (J). The calorie, 4.186 J, is an older unit still seen in some questions.

What is the difference between heat and temperature?

Heat is energy transferred because of a temperature difference, measured in joules. Temperature measures how hot a body is, in kelvin or degrees Celsius.

What is specific heat capacity?

It is the heat needed to raise 1 kg of a substance by 1 K. For water it is about 4186 J/(kg K).