at certain altitude in the upper atmosphere, the temperature is estimated to be -100 degree celsius and the density just 10^-9 that of the earth's atmosphere at STP. Assuming a uniform atmosphere at STP. Assuming a uniform atmospheric composition, what is the pressure, in Torricelli, at this altitude.
To determine the pressure at a certain altitude in the upper atmosphere, we can use the barometric formula, which relates pressure to altitude. The formula is as follows:
P = P0 * exp(-M * g * h / (R * T))
Where:
P = Pressure at the given altitude
P0 = Pressure at sea level (STP)
M = Molar mass of the air
g = Acceleration due to gravity
h = Altitude
R = Ideal gas constant
T = Temperature at the given altitude
In this case, we are given that the temperature at the altitude is -100 degrees Celsius, which we need to convert to Kelvin:
T = -100 + 273.15 = 173.15 K
We are also informed that the density at this altitude is 10^-9 times the density at STP. Since density is directly proportional to pressure, we can determine the pressure ratio:
P / P0 = (Density / Density0)
P / P0 = (10^-9)
Therefore, the pressure at this altitude is 1/10^9 times the pressure at sea level.
Now, let's assume that the atmospheric composition is uniform. So, the molar mass M remains the same throughout the atmosphere.
We know that the molar mass of air is approximately 29 g/mol. The acceleration due to gravity, g, is approximately 9.8 m/s^2. The ideal gas constant, R, is approximately 8.314 J/(mol·K).
Now we can substitute these values into the barometric formula to calculate the pressure at the given altitude:
P = P0 * exp(-M * g * h / (R * T))
P = P0 * exp(-(29/1000) * (9.8) * h / (8.314 * 173.15))
Since we are given that the pressure at this altitude is in Torricelli, we need to convert the answer to Torricelli units.
1 Torricelli = 133.322 Pa
Therefore, the final step is to convert the calculated pressure from pascals to Torricelli:
Pressure (in Torricelli) = P / 133.322
Let me calculate the final answer for you.