Which equation correctly computes energy required to raise the temperature of a mass by ΔT given its specific heat capacity c?

Which equation correctly computes energy required to raise the temperature of a mass by ΔT given its specific heat capacity c?

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

Answer: (D)

Raising the temperature of a mass requires energy that scales with how much material you have, how easily it heats (the specific heat), and how big the temperature change is. The specific heat capacity c tells you how much energy is needed to raise the temperature of one kilogram by one degree. If c is treated as constant over the interval, the energy input is found by integrating dQ = m c dT, which gives Q = m c ΔT. This makes sense dimensionally: kg × (J/kg·K) × K equals joules, so the units line up to express energy. The other forms mix up the factors or invert the relationship, which would not produce energy in joules. If c were not constant, the general form would be Q = ∫ m c(T) dT, but for constant c the simple product m c ΔT is the correct expression.

Raising the temperature of a mass requires energy that scales with how much material you have, how easily it heats (the specific heat), and how big the temperature change is. The specific heat capacity c tells you how much energy is needed to raise the temperature of one kilogram by one degree. If c is treated as constant over the interval, the energy input is found by integrating dQ = m c dT, which gives Q = m c ΔT. This makes sense dimensionally: kg × (J/kg·K) × K equals joules, so the units line up to express energy. The other forms mix up the factors or invert the relationship, which would not produce energy in joules. If c were not constant, the general form would be Q = ∫ m c(T) dT, but for constant c the simple product m c ΔT is the correct expression.