Question

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

Short answer

The heat capacity in joules:

1. 45.8 g of nitrogen gas = 64.30 J/℃.
2. 1.00 pound of aluminum metal = 406.87 J/℃.

The heat capacity in calories:

1. 45.8 g of nitrogen gas = 15.36 cal/℃.
2. 1.00 pound of aluminum metal = 97.20 cal/℃.

Step-by-step solution

Heat capacity

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.

Heat capacity of nitrogen gas in joules

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/℃..

Heat capacity of nitrogen gas in calories per degree

1 calorie = 4.186 J.

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

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

Heat capacity of aluminum metal in joules

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/℃.

Heat capacity of aluminum metal in calories per degree

1 calorie = 4.186 J.

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

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