Question

Heat energy released by water of mass \(3\,\text{kg}\) when it is cooled by \(20^\circ C\) is \((\text{specific heat capacity of water}=4200\,\text{J kg}^{-1}\text{K}^{-1})\)

• A. \(252000\ \text{J}\)
• B. \(420000\ \text{J}\)
• C. \(52000\ \text{J}\)
• D. \(25200\ \text{J}\)

Hint:

Always use: \[ Q=mc\Delta T \] for heat gain or loss when no phase change occurs.

Answer 1

The Correct Option is A

Step 1: Pick the heat formula.
The heat given out or taken in when something changes temperature is \[ Q = m c \Delta T \] Here $m$ is mass, $c$ is the specific heat, and $\Delta T$ is the temperature change.

Step 2: List the known values.
Mass $m = 3$ kg, specific heat $c = 4200$ J/kg/K, temperature drop $\Delta T = 20$ degrees.
Step 3: Note about the temperature change.
A change of $20^\circ$C is the same size as a change of $20$ K, so we can use $20$ directly.
Step 4: Put values into the formula.
\[ Q = 3 \times 4200 \times 20 \]
Step 5: Multiply step by step.
First $3 \times 4200 = 12600$, then $12600 \times 20 = 252000$.
Step 6: Write the answer.
\[ Q = 252000\,\text{J} \] \[ \boxed{252000\,\text{J}} \]