Which equation correctly represents the heat q in terms of mass m, specific heat capacity c, and temperature change ΔT?

Which equation correctly represents the heat q in terms of mass m, specific heat capacity c, and temperature change ΔT?

• A. q = mcΔT
• B. q = m c ΔT^2
• C. q = ΔT/(mc)
• D. q = m/(cΔT)

Answer: (A)

Heat transferred to a substance depends on how much substance there is, how well it stores heat, and how much its temperature changes. This is captured by q = m c ΔT, where m is the mass, c is the specific heat capacity, and ΔT is the temperature change. The specific heat c tells you how much heat is needed to raise the temperature of a given mass by 1 unit, so multiplying m, c, and ΔT gives the total heat in joules. The units line up: mass times specific heat (J/(kg·K)) times a temperature change (K or °C) yields joules. An expression with ΔT squared would imply heat depends on the square of the temperature change, which isn’t how heat capacity is defined. An expression with ΔT in the denominator would imply heat decreases as the temperature change increases, which contradicts the idea that more heat is needed to produce a larger temperature rise. Expressions where the variables are inverted (for example, using m or c in the denominator) would give the wrong units and the wrong dependence on each quantity.

Heat transferred to a substance depends on how much substance there is, how well it stores heat, and how much its temperature changes. This is captured by q = m c ΔT, where m is the mass, c is the specific heat capacity, and ΔT is the temperature change. The specific heat c tells you how much heat is needed to raise the temperature of a given mass by 1 unit, so multiplying m, c, and ΔT gives the total heat in joules. The units line up: mass times specific heat (J/(kg·K)) times a temperature change (K or °C) yields joules.

An expression with ΔT squared would imply heat depends on the square of the temperature change, which isn’t how heat capacity is defined. An expression with ΔT in the denominator would imply heat decreases as the temperature change increases, which contradicts the idea that more heat is needed to produce a larger temperature rise. Expressions where the variables are inverted (for example, using m or c in the denominator) would give the wrong units and the wrong dependence on each quantity.