Scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. The temperature of the gaseous planet varies linearly with the height of the atmosphere. The delicate instruments on board completely fail at a height of 61.5 kilometers. What is the approximate temperature at this altitude?
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Scientists plan to release a space probe that will enter the atmosphere of a gaseous planet. The temperature of the gaseous planet varies linearly with the height of the atmosphere. The delicate instruments on board completely fail at a height of 61.5 kilometers. What is the approximate temperature at this altitude?
To determine the approximate temperature at an altitude of 61.5 kilometers on the gaseous planet, we can use the information that the temperature varies linearly with height.
To find the temperature, we need at least two data points. Let's assume we have the temperature at two different altitudes, A and B, such that A is the altitude where the instruments fail (61.5 kilometers in this case) and B is another known altitude.
Once we have the temperature at these two altitudes, we can use a simple linear equation to estimate the temperature at the desired altitude (61.5 kilometers).
Since we don't have the specific temperature at altitude B, we can't directly calculate the temperature at 61.5 kilometers. However, we can estimate it by assuming some known values.
Let's say we know the temperature at sea level or at the surface of the gaseous planet. In that case, we can assume the temperature and the altitude at sea level to be our data points A and B, respectively.
The average temperature at sea level on Earth is approximately 15 degrees Celsius (288 Kelvin). And we assume the height at sea level to be 0 kilometers.
Now, we need to know the temperature lapse rate, which tells us how much the temperature changes with an increase in altitude. This value helps us calculate the temperature at higher altitudes.
The temperature lapse rate can vary depending on the atmospheric conditions, but a common value used as an approximation is 6.5 degrees Celsius per kilometer.
Using this information, we can calculate the temperature at altitude B (the assumed sea level temperature) as follows:
Temperature at B = Temperature at A + lapse rate * (Altitude at B - Altitude at A)
Temperature at B = 288 Kelvin + 6.5 degrees Celsius per kilometer * (0 kilometers - (-61.5 kilometers))
Temperature at B = 288 Kelvin + 6.5 degrees Celsius per kilometer * 61.5 kilometers
Temperature at B = 288 Kelvin + 399.75 degrees Celsius
Temperature at B = 288 Kelvin + 399.75 Kelvin (converting degrees Celsius to Kelvin)
Temperature at B = 687.75 Kelvin
Therefore, based on the assumptions made, the approximate temperature at an altitude of 61.5 kilometers on the gaseous planet is 687.75 Kelvin.