Changing Units of a Function I have the following function for specific heat (c) in terms of temperature (T), expressed in cal/mol: 
C(T) = A+BT     [cal/mol K] 
I also know that the substance associated with this function has a molar mass of 44g/mol
How can I convert the units of this function to [KJ/Kg K]?
I know the conversion between both units is a factor of 4.18/44 = 0.095, but I could not just multiply this number times A and B, or could I?
 A: If I understand your question correctly, the specific heat is a linear function of the temperature. The specific heat is expressed in [cal/mol K] but you want it expressed in [KJ/Kg K]. So you have a conversion factor from mol to g which is 44g/mol. And you have a conversion factor from cal to kJ which is 0.00418kJ/cal. 
First, note that the coefficients A and B will have their units as well. The units of A are the same as those of the specific heat. But B is multiplied by the temperature to give specific heat, therefore B has units [cal/mol K²]. Not that this is hardly relevant in a sense, because you don't change the temperature units, only the other units. Therefore, the conversion factor for A and B will be the same.
Second, be careful, you have a conversion factor 44g/mol, but you need to go from mol to kg . Therefore, your conversion factor should be 0.044kg/mol.
Thus, going from units [cal/mol K] to [KJ/Kg K], we need to multiply by a conversion factor with units [KJ mol/cal Kg]=[KJ/cal][mol/kg]=[KJ/cal]/[kg/mol]. Which means a factor of
$$\frac{0.00418}{0.044}=0.095$$
numerically.
