Definition:Calorie

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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
\(\ds \) \(\approx\) \(\ds 0 \cdotp 00396 \, 71\) 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