Answer:
The mass of the air in the living room is \( 73.5 \, \text{kg} \) and its weight is approximately \( 720.135 \, \text{N} \).
Explanation:
To find the mass of the air in the living room, you need to calculate the volume of the room first. Then, using the density of air at room temperature and pressure, you can find the mass. Finally, you can calculate the weight of the air using the formula \( \text{weight} = \text{mass} \times \text{gravity} \).
1. **Calculate the volume of the room**:
\( \text{Volume} = \text{length} \times \text{width} \times \text{height} \)
\( \text{Volume} = 4.0 \, \text{m} \times 5.0 \, \text{m} \times 3.0 \, \text{m} = 60.0 \, \text{m}^3 \)
2. **Find the mass of the air**:
The density of air at room temperature and pressure is approximately \( 1.225 \, \text{kg/m}^3 \).
\( \text{Mass} = \text{density} \times \text{volume} \)
\( \text{Mass} = 1.225 \, \text{kg/m}^3 \times 60.0 \, \text{m}^3 = 73.5 \, \text{kg} \)
3. **Calculate the weight of the air**:
Gravity is approximately \( 9.81 \, \text{m/s}^2 \) on Earth.
\( \text{Weight} = \text{mass} \times \text{gravity} \)
\( \text{Weight} = 73.5 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 720.135 \, \text{N} \)
So, the mass of the air in the living room is \( 73.5 \, \text{kg} \) and its weight is approximately \( 720.135 \, \text{N} \).