<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Skip Navigation
Our Terms of Use (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use.

Specific Heat Calculations

Calculating the heat required to raise the temperature of a unit mass by a given amount

Atoms Practice
Estimated7 minsto complete
Practice Specific Heat Calculations
Estimated7 minsto complete
Practice Now
Turn In
Specific Heat Calculations

Water has a very high heat capacity, which makes it useful for radiators

Credit: Adrian Pingstone (Wikimedia: Arpingstone)
Source: http://commons.wikimedia.org/wiki/File:Flat.six.honda.valkyrie.arp.750pix.jpg
License: CC BY-NC 3.0

Does water have a high capacity for absorbing heat?

Yes. In a car radiator, it serves to keep the engine cooler than it would otherwise run. (In the picture above, the radiator is the black object on the left.) As the water circulates through the engine, it absorbs heat from the engine block. When it passes through the radiator, the cooling fan and the exposure to the outside environment allow the water to cool somewhat before it makes another passage through the engine.

Specific Heat Calculations

The specific heat of a substance can be used to calculate the temperature change that a given substance will undergo when it is either heated or cooled. The equation that relates heat \begin{align*}(q)\end{align*}(q) to specific heat \begin{align*}(c_p)\end{align*}(cp), mass \begin{align*}(m)\end{align*}(m), and temperature change \begin{align*} (\Delta{T})\end{align*}(ΔT) is shown below.

\begin{align*}q=c_p \times m \times \Delta{T} \end{align*}q=cp×m×ΔT

The heat that is either absorbed or released is measured in joules. The mass is measured in grams. The change in temperature is given by \begin{align*}\Delta{T}= T_f - T_i\end{align*}ΔT=TfTi, where \begin{align*}T_f\end{align*}Tf is the final temperature and \begin{align*}T_i\end{align*}Ti is the initial temperature.

Sample Problem: Calculating Specific Heat

A 15.0 g piece of cadmium metal absorbs 134 J of heat while rising from 24.0°C to 62.7°C. Calculate the specific heat of cadmium.

Step 1: List the known quantities and plan the problem.


  • heat = \begin{align*}q\end{align*}q = 134 J
  • mass = \begin{align*}m\end{align*}m = 15.0 g
  • \begin{align*}\Delta{\text{T}} = 62.7^\circ \text{C} - 24.0^\circ \text{C} = 38.7^\circ \text{C}\end{align*}ΔT=62.7C24.0C=38.7C


  • \begin{align*}c_p \ \text{of cadmium}= ? \ \text{J}/ \text{g}^\circ \text{C} \\\end{align*}cp of cadmium=? J/gC

The specific heat equation can be rearranged to solve for the specific heat.

Step 2: Solve.

\begin{align*}c_p=\frac{q}{m \times \Delta{T}}=\frac{134 \text{ J}}{15.0 \text{ g} \times 38.7^\circ \text{C}}=0.231 \text{ J/g}^\circ \text{C}\end{align*}cp=qm×ΔT=134 J15.0 g×38.7C=0.231 J/gC

Step 3: Think about your result.

The specific heat of cadmium, a metal, is fairly close to the specific heats of other metals. The result has three significant figures.

Since most specific heats are known, they can be used to determine the final temperature attained by a substance when it is either heated or cooled. Suppose that a 60.0 g sample of water at 23.52°C was cooled by the removal of 813 J of heat. The change in temperature can be calculated using the specific heat equation.

\begin{align*}\Delta{T}=\frac{q}{c_p \times m}=\frac{813 \text{ J}}{4.18 \text{ J/g}^\circ \text{C} \times 60.0 \text{ g}}=3.24^\circ \text{C} \end{align*}ΔT=qcp×m=813 J4.18 J/gC×60.0 g=3.24C

Since the water was being cooled, the temperature decreases. The final temperature is:

\begin{align*}T_f=23.52^\circ \text{C} - 3.24^\circ \text{C}=20.28^\circ \text{C}\end{align*}Tf=23.52C3.24C=20.28C




  • Specific heat calculations are illustrated.


  1. Do different materials have different specific heats?
  2. How does mass affect heat absorbed?
  3. If we know the specific heat of a material, can we determine how much heat is released under a given set of circumstances?

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

  1. [1]^ Credit: Adrian Pingstone (Wikimedia: Arpingstone); Source: http://commons.wikimedia.org/wiki/File:Flat.six.honda.valkyrie.arp.750pix.jpg; License: CC BY-NC 3.0

Explore More

Sign in to explore more, including practice questions and solutions for Specific Heat Calculations.
Please wait...
Please wait...