AcademyTemperature and Heat
Academy
Heat as Energy Transfer
Level 1 - Physics topic page in Temperature and Heat.
Principle
Heat is energy transferred because of a temperature difference.
An object does not contain heat. It contains internal energy, and heat is one way that energy crosses the boundary of a system.
Notation
\(Q\)
energy transferred as heat
\(\mathrm{J}\)
\(m\)
mass
\(\mathrm{kg}\)
\(c\)
specific heat capacity
\(\mathrm{J\,kg^{-1}\,K^{-1}}\)
\(C\)
heat capacity of an object
\(\mathrm{J\,K^{-1}}\)
\(\Delta T\)
temperature change
\(\mathrm{K}\)
\(P\)
power supplied to the object
\(\mathrm{W}\)
Method
For a single material with no phase change, the temperature change is proportional to the energy added and inversely proportional to the heat capacity.
Object heat capacity
\[C=mc\]
This is the heat required per unit temperature change for the whole object.
Temperature-change energy
\[Q=C\Delta T\]
Specific heat form
\[Q=mc\Delta T\]
Sign convention
\[Q>0\Rightarrow \Delta T>0\quad\text{for }c>0\]
If power is supplied steadily and there is no heat loss, the same relation becomes a rate equation.
Power input
\[P=\frac{dQ}{dt}\]
Temperature rate
\[P=mc\frac{dT}{dt}\]
Heating rate
\[\frac{dT}{dt}=\frac{P}{mc}\]
The sign convention belongs to the chosen system. Heat added to the system is positive; heat removed from it is negative.
Rules
These are the compact relations for heat transfer that changes temperature without a phase change.
Heat capacity
\[C=mc\]
Temperature change
\[Q=mc\Delta T\]
Temperature interval
\[\Delta T=T_f-T_i\]
Heating rate
\[\frac{dT}{dt}=\frac{P}{mc}\]
Examples
Question
How much heat is required to warm
\[0.75\,\mathrm{kg}\]
of water from \[18\,\mathrm{^\circ C}\]
to \[42\,\mathrm{^\circ C}\]
? Use \[c=4190\,\mathrm{J\,kg^{-1}\,K^{-1}}\]
Answer
\[\Delta T=42-18=24\,\mathrm{K}\]
\[Q=mc\Delta T=(0.75)(4190)(24)=7.5\times10^4\,\mathrm{J}\]
Checks
- Heat is energy in transfer, not energy stored in an object.
- Positive \(Q\) means energy enters the chosen system.
- The formula \(Q=mc\\Delta T\) does not include phase changes.
- A large heat capacity means the same heat input gives a smaller temperature change.