Question

How much heat energy (Joules) is required to raise the temperature of $ 120.0\;{\text{g}} $ water from $ - {90^ \circ }{\text{C}} $ to $ - {5^ \circ }{\text{C}}? $

Answer 1

Hint: A substance's heat capacity is the amount of heat required to increase the temperature of the entire substance by one degree. If the mass of the substance is unity, the specific heat capacity or the specific heat is called the heat capacity. We shall substitute the value given into the formula below.

Formula Used:
We will use the following formula to solve the question above
 $ q = mc\Delta T $
Where
 $ q $ is the heat energy
 $ m $ is the mass of the water
 $ c $ is the specific heat of water
 $ \Delta T $ is the change in temperature.

Complete Step-by-Step solution
According to the question, the following information is provided to us
The mass of water, $ m = 120{\text{ g}} = 0.12 {\text{kg}} $
The change in temperature, $ \Delta T = - {5^{\text{o}}}{\text{C}} - \left( { - {{90}^{\text{o}}}{\text{C}}} \right) = 268.15{\text{K}} - 183.15{\text{K}} = 85{\text{K}} $
The specific heat of water is known to be, $ c = 4190{\text{J/kgK}} $
Now, we will use the formula stated above
 $ q = mc\Delta T $
Upon substituting the given values into the formula, we get
 $ q = 0.12{\text{kg}} \times 4190\frac{{\text{J}}}{{{\text{kg \times K}}}} \times 85{\text{K}} $
Upon solving, we get
 $ \therefore q = 42738{\text{J}} $
Therefore, the heat energy (Joules) required to raise the temperature is $ q = 42738{\text{J}} $ .

Additional Information
Heat, often called thermal energy, is a form of energy. Energy can be transformed from one form to another, but it can neither be generated nor destroyed; energy is conserved instead. The higher the temperature of a material in basic thermodynamics, the more thermal energy it possesses. Furthermore, the more of a given substance, the more total thermal energy the material will possess at a given temperature.

Note
We know that a substance increases its temperature when heat energy is absorbed by it. If equivalent masses of different substances are given the same amount of heat, the increase in temperature for each substance is observed to be different. This is due to the fact that heat capacities are different for different substances.