In basic thermodynamics, the relationship Q = m c ΔT is the formula for which physical quantity or process?

Introduction / Context:
The formula Q = m c ΔT appears very frequently in physics and engineering problems involving heating or cooling of substances. It expresses a relationship between the heat supplied or removed, the mass of the substance, its specific heat capacity and the resulting change in temperature. This question checks whether you can correctly interpret what physical quantity or process this formula represents, and distinguish it from related concepts such as enthalpy and latent heat.

Given Data / Assumptions:
- Q represents the amount of heat energy transferred to or from a substance.
- m is the mass of the substance, usually in kilograms or grams.
- c is the specific heat capacity of the substance, a material property.
- ΔT is the change in temperature, final temperature minus initial temperature.
- The formula applies where the substance does not change phase over the temperature range considered.

Concept / Approach:
Specific heat capacity c is defined as the amount of heat required to raise the temperature of unit mass of a substance by 1 degree. When this definition is applied to a mass m undergoing a temperature change ΔT, the total heat required is Q = m c ΔT. This formula therefore gives the heat transfer associated with a temperature change of a given mass, assuming no phase change and constant c over the range. It is not, by itself, the definition of c, which is obtained by rearranging the equation, and it does not represent latent heat, which involves phase changes at constant temperature.

Step-by-Step Solution:
Step 1: Recall the definition of specific heat capacity: c is heat needed per unit mass per unit temperature rise. Step 2: From this, write Q for a finite mass and temperature change as Q = m c ΔT. Step 3: Recognise that Q is the heat transferred to change the temperature of the mass m by ΔT without a phase change. Step 4: Understand that enthalpy change is a broader concept which can include phase changes and other effects; Q = m c ΔT is a special case. Step 5: Note that latent heat of vaporization uses a different form, Q = m L, with no temperature change while the phase changes. Step 6: Conclude that the formula most directly represents the heat transferred due to a temperature change in a substance of mass m using specific heat capacity.

Verification / Alternative check:
As a check, consider heating 2 kg of water with c approximately 4200 J kg^-1 K^-1 through 10 degrees. Using Q = m c ΔT gives Q = 2 * 4200 * 10 = 84000 J. This is clearly a calculation of heat transfer. If the same water were boiling at constant temperature, the appropriate formula would involve latent heat, not a temperature difference. This confirms that Q = m c ΔT is linked to sensible heating or cooling, not to latent heat or general enthalpy changes in all processes.

Why Other Options Are Wrong:
General enthalpy change for any process: Enthalpy can change due to many factors, including pressure and phase change. Q = m c ΔT is only one special case and does not cover all situations.
The numerical value of specific heat capacity itself: Specific heat capacity is defined per unit mass and per degree; the formula must be rearranged to c = Q / (m ΔT) to compute c.
Latent heat of vaporization during a phase change: Latent heat is associated with phase change at constant temperature and uses Q = m L, not Q = m c ΔT.

Common Pitfalls:
Learners sometimes apply Q = m c ΔT even when a phase change is taking place, which is not correct. Another common confusion is to label Q = m c ΔT as the specific heat formula, without specifying that it calculates the heat transferred for a given temperature change. Keeping the roles of Q, m, c and ΔT clear, and remembering the separate form for latent heat, helps avoid misapplication of this important equation.

Final Answer:
The relationship Q = m c ΔT is the formula for heat transferred when the temperature of a mass changes, using specific heat capacity.