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The temperature of an open room of volume 30 m3 increases from 170C to 270C due to the sunshine.  The atmospheric pressure in the room remains 1×105 Pa. If   n_{i}  and  n_{f} are the number of molecules in the room before and after heating, then n_{f}-n_{i}will be :  
Option: 1 −1.61×1023  
Option: 2  1.38×1023  
Option: 3  2.5×1025  
Option: 4 −2.5×1025  

Answers (1)




 PV = nRT                                    

\Rightarrow\ \; n_{i}=\frac{PV}{RT_{i}},\ \; n_{f}=\frac{PV}{RT_{f}}

\Rightarrow\ \; n_{f}-n_{i}=\frac{PV}{R} \left(\frac{1}{T_{f}}-\frac{1}{T_{i}} \right )=\frac{10^{5}\times 30}{8.31}\times\left(\frac{1}{300}-\frac{1}{290} \right )

    n_{f}-n_{i}=\frac{10^{5}\times 30}{8.31}\times\frac{-10}{300\times 290}=\frac{-10^{5}}{290\times 8.31}

change in Number of molecules =\frac{-10^{5}\times6.023\times10^{23}}{290\times 8.31}=-2.5\times 10^{25}

Correct option is 4.

Posted by

vishal kumar

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