To determine the correct equation that represents the energy required to heat a substance, let's analyze each option:
A. [tex]\( Q = m L_{\text{fusion}} \)[/tex]
- This equation is used to calculate the energy required to change a substance from solid to liquid (or vice versa) at its melting point. Here, [tex]\( m \)[/tex] is the mass of the substance and [tex]\( L_{\text{fusion}} \)[/tex] is the latent heat of fusion.
B. [tex]\( Q = m c \Delta T \)[/tex]
- This equation represents the energy required to change the temperature of a substance by a certain amount. In this equation:
- [tex]\( Q \)[/tex] is the heat energy,
- [tex]\( m \)[/tex] is the mass of the substance,
- [tex]\( c \)[/tex] is the specific heat capacity of the substance,
- [tex]\( \Delta T \)[/tex] is the change in temperature.
C. [tex]\( Q = m c T \)[/tex]
- This equation is similar but not correct for heating a substance, since [tex]\( T \)[/tex] here is not specified as a change in temperature. Therefore, it does not accurately represent the process of heating.
D. [tex]\( Q = m L_{\text{vapor}} \)[/tex]
- This equation is used to calculate the energy required to change a substance from liquid to gas (or vice versa) at its boiling point. Here, [tex]\( m \)[/tex] is the mass of the substance and [tex]\( L_{\text{vapor}} \)[/tex] is the latent heat of vaporization.
From this analysis, the correct equation representing the energy required to heat a substance, considering a temperature change, is:
[tex]\[ B. \ Q = m c \Delta T. \][/tex]
Thus, the answer is:
[tex]\[ \boxed{B} \][/tex]
