If a balloon containing 1000 L of gas at 50 degrees Celsius and 101.3 kPa rises to an altitude where the pressure is 27.5 kPa and the temperature is 10 degrees Celsius, its volume there is?
Thank You!
To find the volume of the balloon at the given conditions, we can use the combined gas law equation:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = Initial pressure of the gas (101.3 kPa)
V1 = Initial volume of the gas (1000 L)
T1 = Initial temperature of the gas (50 degrees Celsius)
P2 = Final pressure of the gas (27.5 kPa)
T2 = Final temperature of the gas (10 degrees Celsius)
V2 = Final volume of the gas (unknown)
Now let's substitute the given values into the equation and solve for V2:
(101.3 kPa * 1000 L) / (50 + 273.15 K) = (27.5 kPa * V2) / (10 + 273.15 K)
Simplifying the equation:
(101.3 kPa * 1000 L) / (323.15 K) = (27.5 kPa * V2) / (283.15 K)
To solve for V2, cross-multiply and rearrange the equation:
(27.5 kPa * V2) = (101.3 kPa * 1000 L * 283.15 K) / (323.15 K)
V2 = (101.3 kPa * 1000 L * 283.15 K) / (323.15 K * 27.5 kPa)
V2 ≈ 802.22 L
Therefore, the volume of the balloon at the given conditions would be approximately 802.22 L.
To find the volume of the balloon at the new altitude, we can use the combined gas law equation:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ = initial pressure = 101.3 kPa
V₁ = initial volume = 1000 L
T₁ = initial temperature in Kelvin = 50 + 273.15 = 323.15 K
P₂ = final pressure = 27.5 kPa
T₂ = final temperature in Kelvin = 10 + 273.15 = 283.15 K
V₂ = final volume (what we're trying to find)
Let's plug in the values and solve for V₂:
(101.3 kPa * 1000 L) / (323.15 K) = (27.5 kPa * V₂) / (283.15 K)
Now, cross multiply and rearrange the equation to isolate V₂:
V₂ = (27.5 kPa * V₁ * 283.15 K) / (101.3 kPa * 323.15 K)
V₂ ≈ (27.5 kPa * 1000 L * 283.15 K) / (101.3 kPa * 323.15 K)
Calculating this, we get:
V₂ ≈ 770.29 L
Therefore, the volume of the balloon at the new altitude is approximately 770.29 L.
(P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.