Question

1 calorie is equal to:
A. 2.18 joules
B. 3.18 joules
C. 4.18 joules
D. 5.18 joules

Answer 1

- Hint: 1 calorie is defined as the amount of heat energy that is required to raise the temperature of 1 gram of water by $1^{\circ}C$. The relation between calories and joules is merely an empirical one and hence cannot be mathematically derived unless physically experimented upon. Both calorie and joules are units that are used to measure heat energy.


Complete step-by-step solution
Let us try and understand what calorie and joule mean.
Both calorie and joule are units of energy. However, calorie is the unit of energy in the metric system in general, but joule is the SI unit of energy.
A calorie (cal) is defined as the amount of heat energy required to raise the temperature of 1 gram of water by $1^{\circ}C$. It is also sometimes defined as the amount of heat energy required to raise the temperature of 1 kilogram of water by $1^{\circ}C$, but this is called a kilocalorie.
Therefore, $1\;(kcal)\; kilocalorie = 1000\;(cal)\;calories$
A joule (J) is more versatile and is used as units of not only energy but also heat and work. It is defined as the amount of energy transferred to/work done on an object when a force of one newton acts on that object through a distance of one metre ($1\;Nm$). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second.
The value of calories in joules cannot be mathematically proven but can be physically and experimentally observed. It is more of an empirical deduction than a mathematical result.
One way to do this would be to perform a certain amount of mechanical work (in joules), convert the work into heat (possible if the work setup consists of a mechanical stirrer in a fluid, for example), measure the temperature rise, use specific heat to calculate heat energy (in calories).
Therefore, from all the experiments done so far, the agreed upon value to equate calories with joules is:
$1\; calorie = 4.18 \; joules$ or $1\;joule = 0.238\;calories$
Therefore, the correct option would be C. 4.18 joules

Additional Information:
It is interesting to note that the unit (kcal) came into being before (cal).
The (kcal) was first introduced during 1819-1824 by Nicolas Clement whereas the (cal) was introduced in 1852 by Pierre Favre and Johann Silbermann.
The term joule however, was adopted in 1889.

Note: The calorie, in general, is ill-defined since the energy required to raise the temperature of 1 gram of water by $1^{\circ}$C is not always constant! In fact, it varies as a function of water temperature.
The amount of energy required to warm 1 gram of air-free water:
From $3.5^{\circ}C$ to $4.5^{\circ}C$ is called the $4^{\circ}$ calorie = $4.204\;J$
From $14.5^{\circ}C$ to $15.5^{\circ}C$ is called the $15^{\circ}$ calorie = $4.1855\;J$
From $19.5^{\circ}C$ to $20.5^{\circ}$C is called the $20^{\circ}$ calorie = $4.204\;J$
So the value that we have chosen from the question is another type called the Thermochemical calorie.