A weather balloon is inflated to a volume of 27.0 at a pressure of 730 and a temperature of 31.3. The balloon rises in the atmosphere to an altitude, where the pressure is 365 and the temperature is -14.6.

use as a ideal gas behavior

See my post below. No units, no solution.

To solve this problem, we can use the ideal gas law, which relates the pressure, volume, and temperature of a gas. The formula for the ideal gas law is:

PV = nRT

Where:
P is the pressure of the gas (in Pascals)
V is the volume of the gas (in cubic meters)
n is the number of moles of gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature of the gas (in Kelvin)

We can use this formula to find the number of moles of gas before and after the balloon rises in the atmosphere. Once we have the number of moles, we can calculate the final volume of the balloon using the final pressure and temperature.

Step 1: Convert the temperatures to Kelvin
To use the ideal gas law, we need to convert the temperatures from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature.

Initial temperature: 31.3°C + 273.15 = 304.45 K
Final temperature: -14.6°C + 273.15 = 258.55 K

Step 2: Calculate the number of moles of gas before and after the balloon rises
Using the ideal gas law, we can rearrange the equation to solve for the number of moles:

n = PV / RT

The final volume of the balloon is given as 27.0 L, so we need to convert it to cubic meters:

Initial volume: 27.0 L = 0.027 m^3

Now we can calculate the number of moles before the balloon rises:

n1 = (P1 * V1) / (R * T1)
= (730 Pa * 0.027 m^3) / (8.314 J/(mol·K) * 304.45 K)

Similarly, we can calculate the number of moles after the balloon rises:

n2 = (P2 * V2) / (R * T2)
= (365 Pa * V2) / (8.314 J/(mol·K) * 258.55 K)

Step 3: Calculate the final volume of the balloon
Now that we have the number of moles of gas after the balloon rises, we can calculate the final volume of the balloon using the ideal gas law:

V2 = (n2 * R * T2) / P2

Substituting the values:

V2 = (n2 * 8.314 J/(mol·K) * 258.55 K) / 365 Pa

Simplifying the equation will give us the final volume of the balloon.

By following these steps and using the ideal gas behavior, we can determine the final volume of the weather balloon after it rises in the atmosphere.