Answer
I) $1.005 \frac{kJ}{kg.K} $
II) $ 1.005 \frac{J}{g.^{\circ}C} $
III) $ 0.240 \frac{kcal}{kg.^{\circ}C} $
IV) $ 0.240\frac{BTU}{lbm.^{\circ}F} $
Work Step by Step
I) Since the specific heat measures the amount of energy required to change the temperature of a given amount of the substance (air), in this case, the temperature unit refers to a temperature interval, not an absolute temperature. Therefore, the conversion factor is $ 1 \frac{^{\circ}C}{K} $:
$ 1.005 \frac{kJ}{kg.^{\circ}C} \times 1 \frac{^{\circ}C}{K} = 1.005 \frac{kJ}{kg.K} $
II) The preffix k refers to a 1000 conversion factor:
$ 1.005 \frac{kJ}{kg.^{\circ}C} \times 1000 \frac{J}{kJ} \times \frac{1}{1000} \frac{kg}{g} = 1.005 \frac{J}{g.^{\circ}C} $
III) $ 1 cal = 4.184 J $, therefore $ 1 kcal = 4.184 kJ $
$ 1.005 \frac{kJ}{kg.^{\circ}C} \times \frac{1}{4.184} \frac{kcal}{kJ} = 0.240 \frac{kcal}{kg.^{\circ}C} $
IV) $1 kJ = 0.9478 BTU $, $ 1 kg = 2.2046 lbm $, and since we're dealing with temperature intervals: $ 1^{\circ}C = 1.8 ^{\circ}F $.
$ 1.005 \frac{kJ}{kg.^{\circ}C} \times 0.9478 \frac{BTU}{kJ} \times \frac{1}{2.2046} \frac{kg}{BTU} \times \frac{1}{1.8} \frac{^{\circ}C}{^{\circ}F} = 0.240\frac{BTU}{lbm.^{\circ}F} $
