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An open vessel at 27^(@)C is heated unti...

An open vessel at `27^(@)C` is heated until `3//5` of the air in it is expelled. Assuming that the volume of the vessel remains constant, find the temperature to which the vessel has been heated.

Text Solution

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Since the vessel is open, its pressure will remain constant.
Let the number of moles of air at `27^(@)C=n`
No. of moles of air left after heating `=n-(3)/(5)n=(2)/(5)n`
`"Now pV=nRT`
`"At "27^(@)C" "pV=nRxx300" ...(i)"`
At higher temperature, T(K)
`pV=(2)/(5)nRT`
Since pV is constant,
`"or "nRxx300=(2)/(5)nRT" ...(ii)"`
`T=(300xx5)/(2)=750K`
`"or "T=750-273`
`=477^(@)C`.
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