Which equation relates heat transfer to mass, specific heat, and temperature change?

• A. Q = m c ΔT^2
• B. Q = m c ΔT
• C. Q = m ΔT
• D. Q = c ΔT

Answer: (B)

Heat transfer depends on how much substance you have, how much energy is needed to raise its temperature (specific heat), and how big the temperature change is. The amount of heat required to raise the temperature of a mass m by ΔT is given by Q = m c ΔT, where c is the specific heat capacity. Here, ΔT is the temperature final minus the initial, and the sign tells you whether heat is added (positive) or removed (negative).

This equation makes sense because c tells you how much energy per unit mass is needed per degree of temperature change. If you double the mass, you need twice as much energy; if you increase the temperature by 1 K, you need as much energy as dictated by c; and if the material has a higher c, it takes more energy to achieve the same ΔT.

Why the other forms aren’t correct: using ΔT^2 would imply energy grows with the square of the temperature change, which isn’t how specific heat is defined. omitting c loses the material’s property that controls how much energy per degree is required. omitting m ignores that more material needs more energy, and omitting ΔT ignores how much the temperature actually changes.

For example, with 2 kg of a substance where c = 1000 J/(kg·K) and a temperature rise of 5 K, the heat added is Q = 2 × 1000 × 5 = 10,000 J.