To determine which equation represents the energy it takes to heat a substance, let's carefully analyze each of the given options:
Option A: [tex]\(Q = m L_{\text{fusion}}\)[/tex]
- This equation represents the energy needed for a phase change from solid to liquid (or vice versa), not for heating a substance. The term [tex]\(L_{\text{fusion}}\)[/tex] denotes the latent heat of fusion, which is the heat required to change 1 kg of a substance from solid to liquid at its melting point.
Option B: [tex]\(Q = m c \Delta T\)[/tex]
- This equation is used to calculate the heat energy required to change the temperature of a substance. Here, [tex]\(Q\)[/tex] is the heat energy, [tex]\(m\)[/tex] is the mass of the substance, [tex]\(c\)[/tex] is the specific heat capacity, and [tex]\(\Delta T\)[/tex] is the change in temperature. This is the correct equation for heating a substance.
Option C: [tex]\(Q = m L_{\text{vapor}}\)[/tex]
- This equation represents the energy needed for a phase change from liquid to gas (or vice versa). The term [tex]\(L_{\text{vapor}}\)[/tex] denotes the latent heat of vaporization, which is the heat required to change 1 kg of a substance from liquid to gas at its boiling point.
Option D: [tex]\(Q = m c T\)[/tex]
- This equation is similar to Option B but incorrect because it uses [tex]\(T\)[/tex] (temperature) instead of [tex]\(\Delta T\)[/tex] (change in temperature). The temperature itself is not a measure of the change in thermal energy.
Given the detailed analysis, the correct equation to represent the energy it takes to heat a substance is:
[tex]\[
Q = m c \Delta T
\][/tex]
Therefore, the correct option is B.
