a helium balloon is partially filled with 28.7 L of gas at 25.0 degress celcius and a pressure of 1 atm. if the balloon is released and it floats up intp the atmosphere to a heightwhere the pressure is 2.8 x 10^-3 atm and the temperature is -24.0 degrees celcius, calculate the new volume ofthe balloon

First, note the correct spelling of celsius.

Use (P1V1/T1) = (P2V2/T2)
Don't forget that T must be in kelvin.

To calculate the new volume of the balloon, we can use the combined gas law equation:

(P1 × V1) / (T1) = (P2 × V2) / (T2)

Where:
P1 = initial pressure of the gas (1 atm)
V1 = initial volume of the gas (28.7 L)
T1 = initial temperature of the gas (25.0 °C + 273.15 = 298.15 K)
P2 = final pressure of the gas (2.8 x 10^-3 atm)
V2 = new volume of the gas (to be calculated)
T2 = final temperature of the gas (-24.0 °C + 273.15 = 249.15 K)

Now, let's plug in the values and solve for V2:

(1 atm × 28.7 L) / (298.15 K) = (2.8 x 10^-3 atm × V2) / (249.15 K)

(28.7 L × 249.15 K) = (2.8 x 10^-3 atm × V2 × 298.15 K)

V2 = (28.7 L × 249.15 K) / (2.8 x 10^-3 atm × 298.15 K)
V2 ≈ 2554.86 L

Therefore, the new volume of the balloon when it reaches the specified height is approximately 2554.86 L.

To solve this problem, we can use the ideal gas law equation. The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.

We can use the ideal gas law to compare the initial and final conditions of the helium balloon.

Initial conditions:
- Pressure (P1) = 1 atm
- Volume (V1) = 28.7 L
- Temperature (T1) = 25.0 degrees Celsius

Final conditions:
- Pressure (P2) = 2.8 x 10^-3 atm
- Temperature (T2) = -24.0 degrees Celsius

To facilitate the calculation, we need to convert the temperatures from Celsius to Kelvin. The Kelvin temperature scale is an absolute temperature scale where 0 Kelvin (K) is equivalent to -273.15 degrees Celsius. To convert Celsius to Kelvin, we add 273.15 to the Celsius temperature.

Converting the temperatures:
T1 = 25.0 + 273.15 = 298.15 K
T2 = -24.0 + 273.15 = 249.15 K

Now we can use the ideal gas law equation to calculate the new volume (V2) of the balloon:

P1 * V1 / T1 = P2 * V2 / T2

Substituting the values:
1 atm * 28.7 L / 298.15 K = (2.8 x 10^-3 atm) * V2 / 249.15 K

Simplifying the equation:
V2 = (1 atm * 28.7 L * 249.15 K) / (2.8 x 10^-3 atm * 298.15 K)

Calculating the value of V2:
V2 = (28.7 L * 249.15 K) / (2.8 x 10^-3)

V2 ≈ 2,551.91 L

Therefore, the new volume of the balloon at the higher altitude is approximately 2,551.91 L.