Question

How many calories of energy must be added to a 1 gram of water to increase its temperature by 1 degree?

Answer 1

Hint: A calorie is a unit of heat energy. The amount of energy required to raise the temperature of 1 g of a substance by 1 degree Celsius is known as the specific heat of that substance.

Formula Used: \[{\text{q = ms}}\Delta T\]

Complete step-by-step answer:As heat is formed energy can be measured using different units of energy. One of the units of measurement of energy is calories. Here we have to determine the calories of energy that must be added to a 1 gram of water to increase its temperature by 1 degree.
The equation of heat, related to mass, specific heat capacity and the temperature difference is as follows:
\[{\text{q = ms}}\Delta T\]
Here,
\[{\text{q}}\]= heat
\[{\text{m}}\] = mass
\[{\text{s}}\] = specific heat capacity
\[\Delta T = {T_f} - {T_i}\]
Specific heat capacity is the amount of heat required to raise the temperature of 1g of a substance by\[{\text{1}}^\circ {\text{C}}\].
The specific heat of water is \[{\text{1 cal/g }}^\circ {\text{C}}\]
Here we have given the mass of water as 1 g, the standard value of specific heat of water is \[{\text{1 cal/g }}^\circ {\text{C}}\] . As we have to increase the temperature of water by \[1^\circ {\text{C}}\] so we can say that the value of the temperature difference \[\Delta T\] is \[1^\circ {\text{C}}\].
Now, using all given data we can calculate calories of energy needed to add to raise the temperature of 1 g of water by \[1^\circ {\text{C}}\] as follows:
\[{\text{q = 1 g }} \times {\text{1 cal/g }}^\circ {\text{C}} \times 1^\circ {\text{C}}\]
\[{\text{q = 1 cal}}\]
Thus, we can say that 1 cal of energy must be added to a 1 gram of water to increase its temperature by 1 degree.

Note:The law of conservation of energy states that energy neither be created nor be destroyed. It converts from one form to another form Number of calories needed to add to raise the temperature of 1 g of any substance by \[1^\circ {\text{C}}\]is nothing but its specific heat capacity. The specific heat capacity value of a different substance is different.