What units express specific heat capacity?

Hint: Specific heat capacity is the amount of heat that is required by any substance to raise the temperature of 1 kilogram of that substance by 1 Kelvin. Through the formula of specific heat capacity, and the units of the species in the formula, we can derive the expression for the unit of specific heat capacity.

Complete answer:
Units are the measuring standards for the measurement of a particular quantity. Specific heat capacity is the heat required to raise the temperature of 1 kg of any substance by 1 Kelvin. So, the specific heat capacity can be measured by the formula,
$C=\dfrac{q}{m\Delta T}$, where $C$ is the specific heat capacity, $q$ is the heat required, m is the mass of the substance, and $\Delta T$ is the temperature change.
Now, putting the SI units of heat, mass, and temperature in this formula, we can derive the expression for the unit of specific heat capacity as,
$C=\dfrac{Joule}{Ki\log ram\cdot Kelvin}$ as, SI unit of heat is joule, mass is kilogram and temperature is Kelvin, we have,
$C=\dfrac{J}{Kg.K}$, unit of specific heat capacity as joules per kilogram per Kelvin
Hence, the unit of specific heat capacity is $J\,k{{g}^{-1}}{{K}^{-1}}$ .
The other units when temperature is in degree Celsius is, $C=\dfrac{Cal}{g.{}^\circ C}$, which is calorie per gram per degree Celsius, $Cal\,{{g}^{-1}}{}^\circ {{C}^{-1}}$
Hence, the units of specific heat capacity in Kelvin are $J\,k{{g}^{-1}}{{K}^{-1}}$, while in degree Celsius is $Cal\,{{g}^{-1}}{}^\circ {{C}^{-1}}$.

Note:
Another unit of specific heat capacity, where temperature is expressed in Fahrenheit is, $C=\dfrac{BTU}{lb.{}^\circ F}$, where BTU is the heat in British thermal unit, lb is the mass in pounds, and temperature is in degree Fahrenheit. So the unit is $BTU\,l{{b}^{-1}}{}^\circ {{F}^{-1}}$, BTU per pound per degree Fahrenheit.