A block of aluminum is heated electrically by a 30 w heater if the temperature rises by 10°c in 5 minutes, the heat capacity of the aluminum is

Analyze the question: A 30 W heater warms an aluminum block by 10°C in 5 minutes. We need the heat capacity of the block, which is the heat needed to raise its temperature by 1 K.

Concept:

• Energy supplied: E = P × t
• Heat capacity: C = Q / Δθ (unit: J K⁻¹)
• This assumes all the electrical energy goes into heating the block.

Solution:

1. Convert the time to seconds: t = 5 × 60 = 300 s

2. Calculate the energy supplied: Q = P × t = 30 × 300 = 9000 J

3. Calculate the heat capacity: C = Q / Δθ = 9000 / 10 = 900 J K⁻¹

Answer: The heat capacity is 900 J K⁻¹, which matches option A.

Tip: Heat capacity (J K⁻¹) differs from specific heat capacity (J kg⁻¹ K⁻¹). Because the question gives no mass, it must be asking for heat capacity, so you use C = Pt/Δθ. Also, always convert minutes to seconds before using watts.