Question

The air inside a hot-air balloon has a temperature of 370 K and a pressure of 101.3 kPa, the same as that of the air outside. Using the composition of air as 78%N2, 21%O2, and 1%Ar, find the density of the air inside the balloon.

a) 0.55 kg/m3

b) 1.20 kg/m3

c) 1.60 kg/m3

d) 2.40 kg/m3

Answer 1

To find the density of the air inside the hot-air balloon, we can use the ideal gas law equation. By calculating the expression, the density of the air inside the balloon is approximately 1.60 kg/m^3.

Step-by-step explanation:

To find the density of the air inside the hot-air balloon, we can use the ideal gas law equation:

density = (pressure * molar mass) / (gas constant * temperature)

Given that the composition of air is 78% N2, 21% O2, and 1% Ar, we can calculate the average molar mass of the air:

average molar mass = (0.78 * molar mass of N2) + (0.21 * molar mass of O2) + (0.01 * molar mass of Ar)

Substituting the values into the equation, we have:

density = (101.3 kPa * average molar mass) / (8.31 J/(mol·K) * 370 K)

By calculating this expression, we find that the density of the air inside the balloon is approximately 1.60 kg/m^3.