Question

How much heat energy is gained when $5\,kg$ of water at ${20^ \circ }\,C$ is brought to its boiling point?
(A) $1680\,KJ$
(B) $1700\,KJ$
(C) $1720\,KJ$
(D) $1740\,KJ$

Answer 1

Hint The boiling point can be determined by using the specific heat formula, and assume that the working fluid is the water and then substituting the density of the water and the specific heat of the specific heat formula, then the boiling point is determined.
Useful formula
The specific heat formula can be given by,
$Q = m{c_p}\Delta T$
Where, $Q$ is the heat energy of the fluid, $m$ is the mass of the fluid, ${c_p}$ is the specific heat at the constant pressure and $\Delta T$ is the change in the temperature.

Complete step by step answer
Given that,
The mass of the fluid is, $m = 5\,kg$,
The temperature of the fluid is, $T = {20^ \circ }\,C$.
Now,
The specific heat formula can be given by,
$Q = m{c_p}\Delta T\,..............\left( 1 \right)$
Assume that the working fluid is the standard fluid water, then substitute the density of the water and the specific heat of the water and the mass of the water and the change in the temperature in the above equation, then the above equation is written as,
$Q = 5 \times \left( {1000 \times 4.2} \right) \times \left( {100 - 20} \right)$
By subtracting the terms in the above equation, then the above equation is written as,
$Q = 5 \times \left( {1000 \times 4.2} \right) \times 80$
By multiplying the terms in the bracket in the above equation, then the above equation is written as,
$Q = 5 \times 4200 \times 80$
By multiplying the terms in the above equation, then the above equation is written as,
$Q = 1680 \times {10^3}\,J$
Then the above equation is also written as,
$Q = 1680\,KJ$
Thus, the above equation shows the boiling point of the water for the given condition.

Hence, the option (A) is the correct answer.

Note The heat energy of the fluid is directly proportional to the mass of the fluid, the specific heat at the constant pressure and the change in the temperature. As the mass of the fluid, the specific heat at the constant pressure and the change in the temperature increases then the heat energy of the fluid increases.