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Question
Compute the temperature at which the r.m.s. speed of nitrogen molecules is 832 m/s. [Universal gas constant, R = 8320 J/k mole K, molecular weight of nitrogen = 28.]
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Solution
Given:-
crms = 832 m/s,
R = 8320 J/k mole K,
M = 28
To find:
R.M.S velocity (crms)
Formula:-
`"c"_(rms)=sqrt((3RT)/M)`
Calculation: From formula,
`832=sqrt((3xx8320xxT)/28)`
`thereforeT=(832xx832xx28)/(3xx8320)`
`T=(832xx28)/30`
`T=776.5 K`
∴ T = 776.5 K or 503.5° C
The r.m.s. speed of nitrogen molecules is 832 m/s at 776.5 K or 503.5° C
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