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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:-

c_{rms} = 832 m/s,

R = 8320 J/k mole K,

M = 28

To find:

R.M.S velocity (c_{rms})

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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