A piece of substance of specific heat capacity 450Jkg ^ -1 k ^ 1 falls through a vertical distance of 20m from…

Analyze the question A body falls from rest through 20 m. All its potential energy is converted into heat on impact, and we need the temperature rise.

Concept

• Potential energy lost: PE = mgh
• Heat gained: Q = mcΔθ
• Since all the energy becomes heat: mgh = mcΔθ

The mass cancels, so:

Δθ = gh / c

Solution

Δθ = (10 × 20) / 450 Δθ = 200 / 450 Δθ = 4/9 ºC

Check: The units work out as (m/s²)(m) / (J kg⁻¹ K⁻¹) = K, so the answer is a temperature change, as expected.

Answer: The rise in temperature is 4/9 ºC, which is option B.

Exam tip: When a falling object's energy turns into heat, the mass always cancels. Remember the shortcut Δθ = gh/c. You can solve it in seconds without being given the mass. Be careful not to flip the fraction, because 9/2 and 9/4 are the typical distractors.