go to the AUS-e-TUTE homepage
home test drill game contact
 

 

Heat Capacity Calculations

Key Concepts

  • The amount of heat energy (q) gained or lost by a substance is equal to the mass of the substance (m) multiplied by its specific heat capacity (Cg) multiplied by the change in temperature (final temperature - initial temperature)

    q = m x Cg x (Tf - Ti)

  • Specific Heat Capacity (Cg) of a substance is the amount of heat required to raise the temperature of 1g of the substance by 1oC (or by 1 K).

  • The units of specific heat capacity are J oC-1 g-1 or J K-1 g-1
Specific Heat Capacities of Some Substances
[Cg (J K-1 g-1 or J oC-1 g-1)]
aluminiumCg = 0.90 waterCg = 4.18
carbonCg = 0.72 ethanol (ethyl alcohol)Cg = 2.44
copperCg = 0.39 sulfuric acid (liquid)Cg = 1.42
leadCg = 0.13 sodium chloride solidCg = 0.85
mercuryCg = 0.14 potassium hydroxide solidCg = 1.18

  • The amount of heat energy gained or lost by a substance can also be calculated for moles of substance:
    q = n x Cn x (Tf - Ti)
    q = amount of heat energy gained or lost by substance
    n = moles of substance
    Cn = molar heat capacity (J oC-1 mol-1 or J K-1 mol-1)
    Tf = final temperature
    Ti = initial temperature

  • Molar Heat Capacity (Cn) of a substance is the amount of heat required to raise the temperature of 1 mole of the substance by 1oC (or by 1 K).
    The units of molar heat capacity are J oC-1 mol-1 or J K-1 mol-1

  • Heats of Reaction can be measured in the laboratory using a simple calorimeter made up of a polystyrene cup (these are appropriate because of their good insulating properties) that is fitted with a lid and a thermometer.

Examples

  1. Calculate the amount of heat needed to increase the temperature of 250g of water from 20oC to 56oC.

    q = m x Cg x (Tf - Ti)
    m = 250g
    Cg = 4.18 J oC-1 g-1 (from table above)
    Tf = 56oC
    Ti = 20oC

    q = 250 x 4.18 x (56 - 20)
    q = 250 x 4.18 x 36
    q = 37 620 J = 38 kJ

  2. Calculate the specific heat capacity of copper given that 204.75 J of energy raises the temperature of 15g of copper from 25o to 60o.

    q = m x Cg x (Tf - Ti)
    q = 204.75 J
    m = 15g
    Ti = 25oC
    Tf = 60oC

    204.75 = 15 x Cg x (60 - 25)
    204.75 = 15 x Cg x 35
    204.75 = 525 x Cg
    Cg = 204.75 ÷ 525 = 0.39 JoC-1 g-1

  3. 216 J of energy is required to raise the temperature of aluminium from 15o to 35oC. Calculate the mass of aluminium.
    (Specific Heat Capacity of aluminium is 0.90 JoC-1g-1).

    q = m x Cg x (Tf - Ti)
    q = 216 J
    Cg = 0.90 JoC-1g-1
    Ti = 15oC
    Tf = 35oC

    216 = m x 0.90 x (35 - 15)
    216 = m x 0.90 x 20
    216 = m x 18
    m = 216 ÷ 18 = 12g

  4. The initial temperature of 150g of ethanol was 22oC. What will be the final temperature of the ethanol if 3240 J was needed to raise the temperature of the ethanol?
    (Specific heat capacity of ethanol is 2.44 JoC-1g-1).

    q = m x Cg x (Tf - Ti)
    q = 3240 J
    m = 150g
    Cg = 2.44 JoC-1g-1
    Ti = 22oC

    3240 = 150 x 2.44 x (Tf - 22)
    3240 = 366 (Tf - 22)
    8.85 = Tf - 22
    Tf = 30.9oC

Practice Questions Homework Checker
For AUS-e-TUTE members:
  1. Click on the Heat Capacity Calculations drill link:
    Heat Capacity Calculations drill
  2. Enter your username and password if prompted.
  3. Click the "New Question" button to begin the drill.
  4. Worked solutions are provided if you need some help!

Not an AUS-e-TUTE Member?

For AUS-e-TUTE members:

Enter mass of substance: g

Enter specific heat capacity: J oC-1 g-1

Enter initial Temperature: oC
Enter final Temperature: oC

Click Calculate:
Calculation:

q = J

To start again click Reset:
advertise on the AUS-e-TUTE website and newsletters
 
 

Search this Site

You can search this site using a key term or a concept to find tutorials, tests, exams and learning activities (games).
 

Become an AUS-e-TUTE Member

 

AUS-e-TUTE's Blog

 

Subscribe to our Free Newsletter

Email email us to
subscribe to AUS-e-TUTE's free quarterly newsletter, AUS-e-NEWS.

AUS-e-NEWS quarterly newsletter

AUS-e-NEWS is emailed out in
December, March, June, and September.

 

Ask Chris, the Chemist, a Question

The quickest way to find the definition of a term is to ask Chris, the AUS-e-TUTE Chemist.

Chris can also send you to the relevant
AUS-e-TUTE tutorial topic page.

 

Related AUS-e-TUTE Topics

Heat (Enthalpy) of Reaction

Defining Enthalpy Change

Manipulating Enthalpy Change Terms

Energy Profiles (diagrams)

Hess's Law (Additivity of Heats of Reaction)

Heat (Enthalpy) of Formation and Reaction

Bond Energy and Heat of Reaction

Latent Heat (Enthalpy)

Heat (Enthalpy) of Combustion

Calorimetry

Fuel Definitions

 
 

Bookmark AUS-e-TUTE

  Bookmark this site!

Bookmark and Share

 
 

© AUS-e-TUTE