At the top of the mountain, the thermometer reads `0^(@)C` and the barometer reads `710 mm Hg`. At the bottom of the mountain the temperature is `30^(@)C` and the pressure is `760 mm Hg`. The ratio of the density of air at the top with that at the bottom is

Options

A. `1:1`
B. `1.04:1`
C. `1:1.04`
D. `1:1.5`

Explanation

To find the ratio of the density of air at the top of the mountain to that at the bottom, we can use the ideal gas law and the relationship between density, pressure, and temperature. Here’s a step-by-step solution:

### Step 1: Convert Temperatures to Kelvin
- At the top of the mountain, the temperature \( T_1 \) is \( 0^\circ C \).
\[ T_1 = 0 + 273 = 273 \, K \]
- At the bottom of the mountain, the temperature \( T_2 \) is \( 30^\circ C \).
...