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# A coffee maker heats $2\;kg$ of water from $15$Celsius to $100$ Celsius. How much thermal energy was required?

Last updated date: 02nd Aug 2024
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Hint:We know that thermal energy or the heat energy is the increase in temperature due to the movement of atoms. Using the given formula, since the mass and the temperature difference is given, we can calculate the thermal energy from the for thermodynamics formula.
Formula used:
$Q=m\times c\times \Delta T$

When an external stimuli is used to increase the temperature of any substance , here coffee, this increase in temperature, results in an increase in kinetic energy of the water molecules. This change in energy is also called heat energy or more commonly known as thermal energy. This thermal energy is represented as the following, $Q=m\times c\times \Delta T$, where, $Q$ is the thermal energy, $m$ is the mass of the substance , $c$ is the specific heat of the substance, water and $\Delta T$ is the change in temperature.
Here, given that $m=2kg$ and $\Delta T= 100-15=85^{\circ}C$
We know, the specific heat of water is$c=4.186 J/gK$
Substituting the values, in $Q=m\times c\times \Delta T$, we get,
$\implies Q=2kg\times 4.186kJ/kgC \times 85 ^{\circ}C$
$\implies Q=712kJ$
Thus the thermal energy or heat energy produced due the temperature increase is $712\;kJ$
The difference Celsius scale and Kelvin scale are linear. The specific heat $c$ is a constant which can be found easily on logarithmic tables books. Also note in the above question, we are converting grams to kilograms and joules to kilojoules hence the fraction is still valid.