2.3 Exercise 13

In car racing, one advantage of mixing liquid nitrous oxide $\left(\text{N}_{2} \text{O}\right)$ with air is that the boiling of the “nitrous” absorbs latent heat of vaporization and thus cools the air and ultimately the fuel-air mixture, allowing more fuel-air mixture to go into each cylinder. As a very rough look at this process, suppose 1.0 mol of nitrous oxide gas at its boiling point, $−88 °\text{C}$, is mixed with 4.0 mol of air (assumed diatomic) at $30 °\text{C}$. What is the final temperature of the mixture? Use the measured heat capacity of $\text{N}_{2} \text{O}$ at $25 °\text{C}$, which is $30.4 \text{J}/\text{mol} °\text{C}$. (The primary advantage of nitrous oxide is that it consists of 1/3 oxygen, which is more than air contains, so it supplies more oxygen to burn the fuel. Another advantage is that its decomposition into nitrogen and oxygen releases energy in the cylinder.)