Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Heat Capacity

The heat capacity of a substance is the amount of heat required to change its temperature by one degree, and has units of energy per degree

Heat Capacity - C - is a characteristic of an object - the amount of heat required to change its temperature by one degree.

• Heat Capacity has the units of energy per degree.

The amount of heat supplied to heat an object can be expressed as:

Q = C dt                     (1)

where

Q = amount of heat supplied (J, Btu)

C= heat capacity of the system or object (J/K, Btu/ oF)

dt = temperature rise (K, °C, oF)

The SI unit for heat capacity is J/K (joule per kelvin). In the English system, the units are British thermal units per pound per degree Fahrenheit (Btu/oF). In some contexts kJ or cal and kcal are used instead of J.

Never use tabulated values of heat capacity without checking the unites of the actual values!

Specific Heat Capacity (c) is the amount of heat required to change the temperature of a mass unit of a substance by one degree. Specific heat is a more common term for the same.

The heat supplied to a mass can be expressed as

dQ = m c dt                               (1)

where

dQ = heat supplied (J, kJ Btu)

m = unit mass (g, kg, lb)

c = specific heat (J/g K, kJ/kg oC, kJ/kg K, Btu/lb oF)

dt = temperature change (K, oC, oF)

(1) can be transferred to express Specific Heat as:

c = dQ / m dt                          (1b)

Example: The specific heat of iron is 0.45 J/(g K), which means that it takes 0.45 Joules of heat to raise one gram of iron by one degree Kelvin.

Specific Heat Gases

There are two definitions of Specific Heat for vapors and gases:

cp = (δh / δT)p - Specific Heat at constant pressure (J/gK)

cv = ( δh / δT)v - Specific Heat at constant volume (J/gK)

For solids and liquids, cp = cv

Use the links to see tabulated values of specific heat of gases, common liquids and fluids, food and foodstuffmetals and semimetals, common solids and other common substances.

Gas Constant

The individual individual gas constant, R, can be expressed as

R = cp - cv                                     (2)

Ratio of Specific Heat

The Ratio of Specific Heat is expressed as

k = cp / cv                                   (3)

Molar Heat Capacity
(Cp) is the amount of heat needed to increase the temperature of one mol of a substance by one degree at constant pressure.
It is expressed in joules per moles per degrees  Kelvin (or Celsius), J/(mol K).

Example: The molar heat capacity of iron is 25.10 J/(mol K), which means that it takes 25.10 Joules of heat to raise 1 mol of iron by 1 degree Kelvin.

Tabulated values of molar heat capacity, Cp, of a lot of organic and inorganic substances can be found in Standard enthalpy of formation, Gibbs free energy of formation, entropy and molar heat capacity of organic substances  and Standard state and enthalpy of formation, Gibbs free energy of formation, entropy and heat capacity, together with ΔH°f, ΔG°f  and S° for the same substances at 25°C.

Converting between Specific heat and Molar heat capacity

The specific heat capacity can be calculated from the molar heat capacity, and vise versa:

cp = Cp / M    and

Cp = cp . M

where

cp = specific heat capacity

Cp = molar heat capacity

M = molar weight of the actual substance (g/mol).

Example: Methanol (with molecular formula CH3OH) has a molar heat capacity, Cp, of 81.1 J/(mol K). What is the specific heat capacity, cp?

First, we calculate (or find) the molar weight of methanol: 1*12.01g/mol C + 4*1.008g/mol H + 1*16.00g/mol O = 32.04 g/mol CH3OH

Then, the specific heat capacity of methanol is:  cp = 81.8 J/(molK) / 32.04 g/mol = 2.53 J/(g K)

Converting between commonly used Units

Example - Heating Aluminum

2 kg of aluminum is heated from 20 oC to 100 oC. Specific heat of aluminum is 0.91 kJ/kg0C and the heat required can be calculated as

dQ = (2 kg) (0.91 kJ/kg0C) ((100 oC) - (20 oC))

= 145.6 (kJ)

Example - Heating Water

One liter of water is heated from 0 oC to boiling 100 oC. Specific heat of water is 4.19 kJ/kg0C and the heat required can be calculated as

dQ = (1 litre) (1 kg/litre) (4.19 kJ/kg0C) ((100 oC) - (0 oC))

= 419 (kJ)

Related Topics

• Thermodynamics - Effects of work, heat and energy on systems
• Basics - The SI-system, unit converters, physical constants, drawing scales and more
• Material Properties - Material properties for gases, fluids and solids - densities, specific heats, viscosities and more

Tag Search

• en: heat capacity capacities specific thermodynamic temperature
• de: Wärmekapazität Kapazitäten spezifische thermodynamische Temperatur

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro .Add the Engineering ToolBox extension to your SketchUp from the SketchUp Pro Sketchup Extension Warehouse!

Privacy

We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Citation

• Engineering ToolBox, (2003). Heat Capacity. [online] Available at: https://www.engineeringtoolbox.com/heat-capacity-d_338.html [Accessed Day Mo. Year].

Modify access date.

. .

Scientific Online Calculator 6 17