A weather balloon is inflated to a volume of 26.5 L at a pressure of 747 mmHg and a temperature of 29.7 C?

2017-01-11 1:28 pm
The balloon rises in the atmosphere to an altitude, where the pressure is 365 mmHg and the temperature is -13.2 C.

Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Please help

回答 (3)

2017-01-16 11:02 am
✔ 最佳答案
P1 x V1 /T1 = P2 x V2 / T2

P1, V1, and T1 are your initial values of pressure, volume and temperature.
P2, etc are your final values.

Use the formula above and solve for V2.
You will get

P1 x V1 x T2 / P2 = V2

Then plug in your numbers and solve with your calculator.
Also, make sure your temperature is in Kelvin (K). You can get this by adding 273 to your temperature C.

Hope this helps! :)
2017-01-11 2:07 pm
Before the balloon rises : P₁ = 747 mmHg, V₁ = 26.5 L, T₁ = (273.2 + 29.7) K = 302.9 K
After the balloon rises : P₂ = 365 mmHg, V₂ = ? L, T₂ = (273.2 - 13.2) K = 260.0 K

For a fixed amount of gas : P₁V₁/T₁ = P₂V₂/T₂
Then, V₂ = V₁ × (P₁/P₂) × (T₂/T₁)

Volume of the balloon at that altitude, V₂ = (26.5 L) × (747/365) × (260.0/302.9) = 46.6 L
2017-01-11 2:11 pm
Use the combined gas equation:
Note Temperature must be in K : 29.7°C = 302.7K , -13.2°C = -13.2 + 273 = 259.8K
There is no need to convert the pressure into other units.
Equation:
P1V1/T1 = P2V2/T2
365*V1 / 259.8 = 747*26.5/302.7
V1 = (259.8*747*26.5) / (365*302.7)
V1 = 46.5L


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