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

Concept:
The quantity of heat energy required to raise the temperature of a substance is given by:
where:

• $Q$ = heat energy (in joules, J)

• $m$ = mass of the substance (in kg)

• $c$ = specific heat capacity of the substance (in J/kg$^\circ$C)

• $\Delta T$ = change in temperature (in $^\circ$C or K)
This formula reflects the fact that more heat is needed for larger masses, for substances with higher specific heat capacity, and for larger temperature changes.

Step 1: Identify all given values.

• Mass of water: $m = 2$ kg.

• Change in temperature: $\Delta T = 5^\circ$C.

• Specific heat capacity of water: $c = 4200$ J/kg$^\circ$C.

Step 2: Substitute into the formula.


Step 3: Compute step by step.



Step 4: Unit analysis to verify.

= kg Jkg ^ ^ = J.
]

Step 5: Verify why other options are wrong.

• (A) 4200 J: This would be the heat for only 1 kg and 1$^\circ$C change (just the specific heat capacity value, not the calculation).

• (B) 420 J: This arises from a computation error, perhaps $2 \times 4200 \div 20 = 420$. Does not fit.

• (D) 42 J: Far too small; this is 1000 times smaller than the correct answer.