Calculate the heat capacity, in joules and in calories per degree, of the following:

(a) 45.8 g of nitrogen gas

(b) 1.00 pound of aluminum metal

The heat capacity of a substance can be calculated by the formula H = mc, where “m” is the mass of the substance and “c” is its specific heat capacity.

From table 5.1, we know that the specific heat capacity of nitrogen gas is 1.040J/g℃.

The mass of the nitrogen gas = 45.8 g (given).

Therefore, the heat capacity of 45.8 g of nitrogen gas in joules = 45.8\( \times \)1.404 = 64.30 J/℃..

1 calorie = 4.186 J.

The heat capacity of 45.8 g of nitrogen gas in calories =

\(\begin{aligned} = \frac{{64.30}}{{4.186}}\\ = 15.36\frac{{cal}}{{^0C}}\end{aligned}\)

From table 5.1, we know that the specific heat capacity of aluminum metal is 0.897J/g℃.

The mass of the aluminum metal = 1 pound (given).

The mass of the aluminum in grams = 453.592 \( \times \)1 = 453.592 g.

Therefore, the heat capacity of 1 pound of aluminum in joules = 453.592 \( \times \) 0.897 = 406.872J/℃.

1 calorie = 4.186 J.

The heat capacity of 1 pound of aluminum in calories is:

\(\begin{aligned} = \frac{{406.872}}{{4.186}}\\ = 97.20\frac{{cal}}{{^0C}}\end{aligned}\).