Definition:Calorie
Definition
The calorie is a CGS unit of heat energy.
It was originally defined as equal to the energy required to raise the temperature of $1$ gram of water by $1 \cels$.
However, it is noted that this energy depends upon the initial temperature of the water itself.
Hence there are a number of different definitions for the calorie:
$4 \cels$ Calorie
The $4 \cels$ calorie is a CGS unit of heat energy.
It is defined as equal to the energy required to raise the temperature of $1$ gram of water from $3 \cdotp 5 \cels$ to $4 \cdotp 5 \cels$ at standard atmospheric pressure.
\(\ds \) | \(\) | \(\ds 1\) | $4 \cels$ calorie | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 4 \cdotp 204\) | joules | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 00398 \, 5\) | British thermal units | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 1 \cdotp 168 \times 10^{-6}\) | kilowatt-hours | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 2 \cdotp 624 \times 10^{19}\) | electron volts |
$15 \cels$ Calorie
The $15 \cels$ calorie is a CGS unit of heat energy.
It is defined as equal to the energy required to raise the temperature of $1$ gram of water from $14 \cdotp 5 \cels$ to $15 \cdotp 5 \cels$ at standard atmospheric pressure.
\(\ds \) | \(\) | \(\ds 1\) | $15 \cels$ calorie | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 4 \cdotp 1855\) | joules | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 3 \cdotp 087\) | foot-pounds | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 00396 \, 71\) | British thermal units | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 1 \cdotp 1626 \times 10^{-6}\) | kilowatt-hours | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 2 \cdotp 6124 \times 10^{19}\) | electron volts |
$20 \cels$ Calorie
The $20 \cels$ calorie is a CGS unit of heat energy.
It is defined as equal to the energy required to raise the temperature of $1$ gram of water from $19 \cdotp 5 \cels$ to $20 \cdotp 5 \cels$ at standard atmospheric pressure.
\(\ds \) | \(\) | \(\ds 1\) | $20 \cels$ calorie | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 4 \cdotp 182\) | joules | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 00396 \, 4\) | British thermal units | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 1 \cdotp 162 \times 10^{-6}\) | kilowatt-hours | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 2 \cdotp 610 \times 10^{19}\) | electron volts |
Mean Calorie
The mean calorie is a CGS unit of heat energy.
It is defined as equal to $\dfrac 1 {100}$ the energy required to raise the temperature of $1$ gram of water from $0 \cels$ to $100 \cels$ at standard atmospheric pressure.
\(\ds \) | \(\) | \(\ds 1\) | mean calorie | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 4 \cdotp 190\) | joules | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 00397 \, 1\) | British thermal units | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 1 \cdotp 164 \times 10^{-6}\) | kilowatt-hours | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 2 \cdotp 615 \times 10^{19}\) | electron volts |
Thermodynamic Calorie
The thermodynamic calorie is a CGS unit of heat energy.
This unit is generally used in chemistry.
It is defined as:
- $4 \cdotp 1840$ joules exactly.
\(\ds \) | \(\) | \(\ds 1\) | thermodynamic calorie | |||||||||||
\(\ds \) | \(=\) | \(\ds 4 \cdotp 1840\) | joules | \(\quad\) (exact) | ||||||||||
\(\ds \) | \(\approx\) | \(\ds 1 \cdotp 1622\) | milliwatt-hours | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 00396 \, 4\) | British thermal units | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 1 \cdotp 162 \times 10^{-6}\) | kilowatt-hours | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 2 \cdotp 611 \times 10^{19}\) | electron volts |
International Calorie
The international calorie is a CGS unit of heat energy.
This unit is generally used in engineering.
It is defined as:
- $1 \cdotp 163$ milliwatt-hours, or $4 \cdotp 1868$ joules exactly.
\(\ds \) | \(\) | \(\ds 1\) | international calorie | |||||||||||
\(\ds \) | \(=\) | \(\ds 4 \cdotp 1868\) | joules | \(\quad\) (exact) | ||||||||||
\(\ds \) | \(=\) | \(\ds 1 \cdotp 163\) | milliwatt-hours | \(\quad\) (exact) | ||||||||||
\(\ds \) | \(\approx\) | \(\ds 0 \cdotp 00396 \, 83\) | British thermal units | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 1 \cdotp 1630 \times 10^{-6}\) | kilowatt-hours | |||||||||||
\(\ds \) | \(\approx\) | \(\ds 2 \cdotp 6132 \times 10^{19}\) | electron volts |
Symbol
- $\mathrm {cal}$
The symbol for the calorie is $\mathrm {cal}$.
However, this is of limited usefulness unless which specific type of calorie is under discussion, for example:
- the thermodynamic calorie, with symbol $\mathrm {cal_c}$
- the international calorie, with symbol $\mathrm {cal_s}$.
The $\LaTeX$ code for \(\mathrm {cal}\) is \mathrm {cal}
.
Also known as
The calorie is also known as the small calorie in order to distinguish it from the large calorie, some $1000$ times larger.
Also see
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): calorie
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): calorie