Concept explainers
Interpretation:
The most probable speed and root mean square speed are to be compared and the value of the final temperature is to be calculated.
Concept Introduction:
The root mean square speed for a molecule can be calculated as:
Here,
The most probable speed can be calculated as:
Here,
Answer to Problem 155AP
Solution:
(a)
The root mean square speed is more than the probable speed for nitrogen at the given temperature.
(b)
The final temperature is
Explanation of Solution
a)Nitrogen at
The most probable speed can be calculated as:
The conversion of temperature from degree Celsius to Kelvin can be done by using the formula given below:
Substitute
The molar mass of nitrogen
Convert gram to kilogram as:
Substitute
On taking the square root, the most probable speed for nitrogen is as:
The root mean square speed for a molecule can be calculated as:
Substitute
On taking the square root, the most probable speed for nitrogen is as:
Hence, the root mean square speed is more than the probable speed for nitrogen at given temperature.
b) Value of
The most probable speed can be calculated as:
From the figure,
At temperature
At temperature
For temperature
For temperature
Now, take the ratio of the most probable speed at temperature
Substitute
Now, on squaring both sides, solve as:
Hence, the final temperatureis
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Chapter 10 Solutions
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