The units of specific heat care J/kg·K, but the units of heat of fusion L_for heat of vaporization L_v are simply J/kg. Why do the units of L_fand L_v not include a factor of (K)^–1 to account for a temperature change?

The unit of specific heat cis J/kg·K. The units of heat of fusion L_f and heat of vaporization L_v are J/kg.

Specific heat of a material is described as the fixed amount of energy required so that 1 gm of the material can increase its temperature by 1° C.

The heat of fusion and the heat of vaporization is the amount of energy the material requires to change its physical form, but the temperature is not an important factor here. Other parameters play an important part in calculating the heat of fusion and the heat of vaporization.

Unit for specific heat is given as,

$\frac{\mathrm{J}}{\mathrm{kg}.°\mathrm{C}}$

Here the essential factor is the temperature unit, as we are calculating specific for a change in temperature by 1 unit.

Unit for the heat of fusion and heat of vaporization is given as,

$\frac{\mathrm{J}}{\mathrm{kg}}$

Here in the case when the material is changing its physical form, the pressure, volume, temperature, and other parameters will be affection the heat of fusion or evaporation. So, the temperature of the system will depend upon the parameters that are affecting the temperature at which the change in physical form took place, but the heat of fusion and heat of evaporation will just depend on the energy required and the amount of the material that was present in the system. If fusion occurred at temperature-1 when parameters are from set -1, and as the parameters are changing, the same fusion might occur at temperature-2 only.

Thus, the units of L_fand L_v will not include a factor of (K)^–1 to account for a temperature change.