Question

A body was supplied 1000 kilocalories of heat. Express this heat in megajoules.

Answer 1

Hint: Recall the basic information about the conversion of units of the physical quantities related to the energy from one unit of energy to the other unit of energy. First convert the heat energy given to the body from kilocalorie to calorie. Then convert the unit of this heat energy from calorie to joule and finally convert the unit of this heat energy from joule to megajoule which is the required answer.

Complete step by step answer:
We have given that the heat supplied to the body is 1000 kilocalories.
\[Q = 1000\,{\text{kcal}}\]
We have asked to convert this heat energy into megajoules or to convert the unit of this given heat energy from kilocalories to megajoule.We know that one kilocalorie (\[1\,{\text{kcal}}\]) of heat energy is equal to \[{10^3}\,{\text{cal}}\].
\[1\,{\text{kcal}} = {10^3}\,{\text{cal}}\]

Let us first convert the unit of the given heat energy from kilocalorie to calorie.
\[Q = \left( {1000\,{\text{kcal}}} \right)\left( {\dfrac{{{{10}^3}\,{\text{cal}}}}{{1\,{\text{kcal}}}}} \right)\]
\[ \Rightarrow Q = {10^6}\,{\text{cal}}\]
We know that the energy of one calorie (\[1\,{\text{cal}}\]) is equivalent to \[4.186\,{\text{J}}\] of energy.
\[1\,{\text{cal}} = 4.186\,{\text{J}}\]
So, now we can convert the unit of given energy to the SI system of units which is joule.
\[ \Rightarrow Q = \left( {{{10}^6}\,{\text{cal}}} \right)\left( {\dfrac{{4.186\,{\text{J}}}}{{1\,{\text{cal}}}}} \right)\]
\[ \Rightarrow Q = 4.186 \times {10^6}\,{\text{J}}\]

We also know that the relation between the units of energy joule and mega joule is
\[1\,{\text{MJ}} = {\text{1}}{{\text{0}}^6}\,{\text{J}}\]
Let us now convert the unit of the given heat energy from joule to megajoule.
\[ \Rightarrow Q = \left( {4.186 \times {{10}^6}\,{\text{J}}} \right)\left( {\dfrac{{1\,{\text{MJ}}}}{{{{10}^6}\,{\text{J}}}}} \right)\]
\[ \therefore Q = 4.186\,{\text{MJ}}\]

Hence, the value of the energy supplied to the body in megajoules is \[4.186\,{\text{MJ}}\].

Note: The students should not get confused between the conversion factor for the conversion of energy from calorie to joule. Sometimes one calorie of energy is considered equal to \[4.2\,{\text{J}}\]. But this is the rounded conversion factor to the nearest round figure value. The actual value of one calorie of energy is equal to \[4.186\,{\text{J}}\].