Question

Find heat required to raise temperature of 2 kg water by 5\(^\circ\)C. (Specific heat of water = 4200 J/kg\(^\circ\)C)

• A. 4200 joules
• B. 420 joules
• C. 42000 joules
• D. 42 joules

Hint:

The formula $Q = mc\Delta T$ is one of the most fundamental equations in thermodynamics. A useful value to remember: the specific heat of water is $4200$ J/kg$^\circ$C (or $4.2$ J/g$^\circ$C), which is very high --- this is why water is such an effective coolant. Always keep track of units: mass in kg, temperature change in $^\circ$C, and $c$ in J/kg$^\circ$C gives $Q$ in Joules.

Answer 1

The Correct Option is C

Step 1: Recall the heat formula.
The heat needed to change the temperature of a substance is $Q = m\,c\,\Delta T$, where $m$ is mass, $c$ is specific heat, and $\Delta T$ is the temperature change.

Step 2: Why this formula works.
More mass, a higher specific heat, or a bigger temperature rise each need more heat. The formula multiplies all three together.

Step 3: List the given values.
Mass $m = 2$ kg, specific heat $c = 4200$ J/kg$^\circ$C, and temperature change $\Delta T = 5\,^\circ$C.

Step 4: Substitute into the formula.
\[ Q = 2 \times 4200 \times 5 \]

Step 5: Multiply step by step.
First $2 \times 4200 = 8400$, then $8400 \times 5 = 42000$.

Step 6: State the result with units.
So the heat required is $42000$ joules. Therefore \[ \boxed{42000\ \text{joules}} \]