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What amount of heat must be supplied to `2xx10^(-2)Kg` of nitrogen at room temperature to rise its temperature by `45^(@)C` at constant pressure? Given molecular mass of nitrogen is 28 and `R=8.3J mol e^(-1)K^(-1)`

Text Solution

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Mass of nitrogen, `m=2.0xx10^(-2)kg=20g`
Rise in temperature, `DeltaT = 45^(@)C`
Molecular mass of `N_(2), M = 28`
Universal gas constant, `R = 8.3 " J "mol^(-1)K^(-1)`
Number of moles, `n=(m)/(M)`
`=(2.0xx10^(-2)xx10^(3))/(28)=0.714`
Molar specific heat at constant pressure for nitrogen, `C_(r)=(7)/(2)R`
`=(7)/(2)xx8.3`
`=29.05" J "mol^(-1)K^(-1)`
The total amount of heat to be supplied is given by the relation:
`DeltaQ=nCpDeltaT`
`=0.714xx29.05xx45`
`=933.38J`
Therefore, the amount of heat to be supplied is 933.38 J.
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