JAMB 2013 Physics · Question 42

Two liquids X and Y having the same mass are supplied with the same quantity of heat. If the temperature rise…

Question

Two liquids X and Y having the same mass are supplied with the same quantity of heat. If the temperature rise in X is twice that of Y, the ratio of specific heat capacity of X to that of Y is

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

Answer: B. 1:2

Explanation written with AI and checked against the answer key

Analyze the question: Two liquids have equal mass and receive equal heat. X's temperature rise is twice Y's. We need c_X : c_Y. Concept: The heat absorbed by a substance is Q = mcΔθ where m is mass, c is specific heat capacity, and Δθ is the temperature rise. Solution: For X: Q = m c_X Δθ_X For Y: Q = m c_Y Δθ_Y Since Q and m are the same for both: m c_X Δθ_X = m c_Y Δθ_Y c_X / c_Y = Δθ_Y / Δθ_X Given Δθ_X = 2Δθ_Y: c_X / c_Y = Δθ_Y / (2Δθ_Y) = 1/2 So c_X : c_Y = 1 : 2. Check: X heats up more for the same heat, so it needs less heat per degree. That means X has the smaller specific heat capacity, which agrees with 1:2. Tip: With equal mass and equal heat, c and Δθ are inversely proportional (c ∝ 1/Δθ). The liquid with the bigger temperature rise has the smaller specific heat capacity. Water has a high c, so it heats up slowly.

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