# Specific Heat Calculator

Created by Luis Hoyos
Last updated: Jul 11, 2022

Welcome to the specific heat calculator (don't confuse it with heat capacity). You can use this tool for various purposes:

• Calculate the specific heat capacity of water and other substances.
• Calculate the energy required to increase the temperature of an amount of substance of known specific heat.
• Calculate the temperature change an energy addition will cause to an amount of substance of known specific heat.
• Calculate the mass required to obtain a temperature change through some energy addition.

## Formula to calculate the specific heat

The definition says specific heat is the energy required to raise the temperature of a unit mass of a substance by one degree. Specific heat is also known as specific heat capacity.

The following equation describes this energy addition:

Q = mc∆T

where:
m — Mass of the substance;
c — Specific heat capacity; and
∆T — Temperature change.

We can solve for c in the Q = mc∆T equation and obtain the formula to explicitly calculate the specific heat:

c = Q/(m∆T)

It's worth mentioning that the previous equation only applies when the energy addition causes a temperature increase. A situation where this doesn't occur is in a phase change process (for example, when reaching the boiling point), in which the energy addition doesn't increase the kinetic energy of the molecules (causing a temperature change) but causes the mentioned phase change.

We call latent energy the energy dedicated to phase change processes, while we call sensible energy what causes a temperature change.

## Specific heat capacity at constant pressure (cₚ) vs. at constant volume (cᵥ)

For the same gas, causing a temperature increase can take two completely different amounts of energy, depending on how we execute the process.

Increasing the energy of a gas at a constant volume (for example, heating a closed rigid gas container) requires less energy than doing it at constant pressure (allowing expansion of the container boundaries). At constant pressure, we don't only need energy for the temperature increase but also for the container expansion that keeps the pressure constant.

For that reason, depending on how we execute the process, we define two types of specific heat:

• Specific heat at constant pressure (cp); and
• Specific heat at constant volume (cv).

For liquids and solids, this also occurs, but the effects are practically negligible because these substances are almost incompressible.

## Specific heat capacity of water and other substances

The following are the values of the specific heat capacity of water and other common substances:

• Ice: 2,100 J/(kg·K)
• Water: 4,200 J/(kg·K)
• Water vapor: 2,000 J/(kg·K)
• Basalt: 840 J/(kg·K)
• Granite: 790 J/(kg·K)
• Aluminum: 890 J/(kg·K)
• Iron: 450 J/(kg·K)
• Copper: 380 J/(kg·K)
Luis Hoyos
Energy (Q)
J
Change of temperature (ΔT)
°C
Mass (m)
kg
Substance (optional)
Custom ▾
Specific heat capacity (c)
J/(kg·K)
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