Which formula represents specific heat capacity given heat energy Q, mass m, and temperature change ΔT?

• A. Q / m
• B. Q / (m × ΔT)
• C. Q × ΔT / m
• D. m × ΔT / Q

Answer: (B)

Specific heat capacity tells us how much energy is needed to raise the temperature of a unit mass by one degree. The relation between heat added, mass, temperature change, and c is Q = m c ΔT. To find c, rearrange this to c = Q / (m ΔT). This means you divide the heat energy by both the mass and the temperature change. The units work out correctly: joules divided by kilograms times degrees Celsius gives J/(kg·°C), which is the standard unit for specific heat capacity.

For example, if 83,680 J of energy raises 2 kg of a substance by 10°C, c = 83,680 / (2 × 10) = 4,184 J/(kg·°C), as for water. Other expressions don’t match this relationship or produce the wrong units (they either omit the dependence on ΔT or mix in ΔT in the numerator).