The specific heat capacity of a substance is the energy per unit mass needed to change its temperature by 1K. The specific latent heat of a substance is the energy needed per unit mass to change its phase.
Equations
description
equation
Specific heat capacity equation
E=mcΔθ
Specific latent heat equation
E=mL
Variable definitions
quantity name
symbol
derived units
alternative units
si base units
energy
E
J
eV
kgm2s−2
mass
m
kg
kg
specificheatcapacity
c
Jkg−1K−1
m2s−2K−1
temperature
T/θ
K
°C
K
specificlatentheat
L
Jkg−1
m2s−2
Specific heat capacity
The specific heat capacity of a substance is defined as the energy needed to change the temperature of 1kg of mass of a substance by 1K. It is symbolised by the letter c and has units Jkg−1K−1.
The energy needed to change the temperature of a substance can be found with the equation:
E=mcΔθ
Note: The Δ means change in the variable in front of it. Also, when you are finding the change in temperature, you can keep the temperature in °C as the change in temperature will be the same in K.
The specific heat capacity of a substance changes depending on its phase. For example, the specific latent of water is different to that of ice.
Specific heat capacity at thermal equilibrium
When there are two materials that are in equilibrium, you can equate the specific heat capacity equation of each substance. This is useful when working out an unknown mass or specific heat capacity.
Example
A steel spatula is used to cook dinner and reaches a temperature of 100°C. The spatula is then placed in 2.0kg of water at 35°C. Eventually the water and the spatula reach thermal equilibrium at 40°C.
Calculate the mass of the spatula. Assume all of the spatula is steel and submerged in the water. The specific heat capacity of steel and water respectively is 420Jkg−1K−1and4200Jkg−1K−1.
Equate the specific heat capacity equation for water and steel:
msteelcsteelΔθsteel=mwatercwaterΔθwater
Rearrange for msteel by dividing by csteelΔθsteel:
msteel=csteelΔθsteelmwatercwaterΔθwater
Substitute in the values and calculate the final answer:
msteel=420×602.0×4200×5=1.66667...kg
The mass of the steel spatula is 1.7kg to 2 significant figures.
Specific latent heat
The specific latent heat is defined as the energy needed to change the phase of 1kg of a substance while at constant temperature. It is symbolised by the letter L and has units Jkg−1.
The energy needed to change the phase of a substance can be found with the equation:
E=mL
There are two types of specific heat capacity which depend on the phase change:
When the substance changes from solid to liquid it is referred to as specific latent heat of fusion Lf.
When the substance changes from liquid to gas it is referred to as specific latent heat of vaporisation Lv.
Example
Calculate the total energy required to turn a 2kg block of ice at −5°C into 20°C water. The specific heat capacity of ice and water are 2000Jkg−1K−1 and 4200Jkg−1K−1 respectively, while the specific latent heat of fusion for ice is 3.3×105Jkg−1.
Calculate the differences between the temperatures:
Δθ(−5°C→0°C)=5°CΔθ(0°C→20°C)=20°C
Substitute all the numbers into the equation:
Etot=2×2000×5+2×3.3×105+2×4200×20
Calculate the total energy:
Etot=8.48×105J=848kJ
The total energy needed to turn a 2kg block of −5°C ice into water at 20°C is 800kJ to one significant figure.
Note: Remember to round your answers to the lowest number of significant figures given.
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Energy transfer by heating
Unit 2
Specific heat capacity
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Specific latent heat and specific heat capacity
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FAQs - Frequently Asked Questions
What is the specific heat capacity of a substance?
The specific heat capacity of a substance is defined as the energy per unit mass required to change its temperature by 1 K.
What is the specific latent heat of a substance?
The specific latent heat of a substance is the energy per unit mass required to change its phase.
What does the specific latent heat of a substance depend on?
The specific latent heat of a substance depends on the phase change occurring, for example the specific latent heat for fusion is different to that of vaporisation,