JAMB 2017 Physics · Question 22

When two objects P and Q are supplied with the same quantity of heat, the temperature change in P is observed…

Question

When two objects P and Q are supplied with the same quantity of heat, the temperature change in P is observed to be twice that of Q. The mass of P is half that of Q. The ratio of the specific heat capacity pf P to Q is

A.1:4
B.4:1
C.1:1
D.2:1

Answer: C. 1:1

Explanation written with AI and checked against the answer key

Analyze the question

Both objects receive the same heat, Q_heat. We know:

ΔθP = 2ΔθQ
mP = ½ mQ
We need cP : cQ

Concept

Heat gained: H = mcΔθ, so c = H / (mΔθ)

Solution

For P: H = mP · cP · ΔθP For Q: H = mQ · cQ · ΔθQ

Since the heat is the same:

mP · cP · ΔθP = mQ · cQ · ΔθQ

cP / cQ = (mQ · ΔθQ) / (mP · ΔθP)

Substitute mP = ½ mQ and ΔθP = 2ΔθQ:

mP · ΔθP = (½ mQ)(2ΔθQ) = mQ · ΔθQ

So:

cP / cQ = (mQ · ΔθQ) / (mQ · ΔθQ) = 1

The ratio is 1 : 1.

Check: The halved mass and doubled temperature change cancel each other, so the specific heat capacities must be equal.

Tip: When the same heat is supplied, the product m × Δθ is inversely proportional to c. Compute m × Δθ for each object first. If the products are equal, the specific heat capacities are equal. Here, ½ × 2 = 1 for P, and 1 × 1 = 1 for Q.

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