A hot air balloon has a volume of 55,287 m3 at 60C, what is its volume at 20C?
(V1/T1) = (V2/T2)
Remember T must be in kelvin.
12.5
To find the volume of a hot air balloon at a different temperature, we can use the ideal gas law.
The ideal gas law equation is:
PV = nRT
Where:
P represents the pressure of the gas
V represents the volume of the gas
n represents the number of moles of the gas
R is the ideal gas constant (8.314 J/(mol·K))
T represents the temperature of the gas in Kelvin (K)
To solve for the volume at 20°C, we need to convert the temperatures to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature.
So, for 60°C, the temperature in Kelvin would be:
T1 = 60°C + 273.15 = 333.15 K
For 20°C, the temperature in Kelvin would be:
T2 = 20°C + 273.15 = 293.15 K
We are given the volume, V1 = 55,287 m^3, at T1 = 333.15 K.
Now, we need to find the volume, V2, at T2 = 293.15 K.
To find the new volume, we can rearrange the ideal gas law equation and solve for V2:
V2 = V1 * (T2 / T1)
Substituting the values into the equation:
V2 = 55,287 m^3 * (293.15 K / 333.15 K)
Now, let's calculate the volume at 20°C.
To find the volume of the hot air balloon at 20°C, we need to apply the ideal gas law. The ideal gas law equation is given by:
PV = nRT
Where:
P = Pressure (constant for this question)
V = Volume
n = Number of moles of gas
R = Ideal gas constant
T = Temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin. To do this, we add 273.15 to the Celsius temperature. So we have:
T1 = 60°C + 273.15 = 333.15 K (Temperature at 60°C)
T2 = 20°C + 273.15 = 293.15 K (Temperature at 20°C)
Next, we can set up the equation using the given volume at 60°C:
PV1 = nRT1
Since the volume and the number of moles stay the same, we can rearrange the equation to find the new volume at 20°C:
V2 = (PV1 * T2) / (n * T1)
However, we don't have information about the pressure or the number of moles of gas. Therefore, we cannot calculate the exact volume at 20°C using the ideal gas law.