The temperature of an open room of ...
Question
The temperature of an open room of volume 30m from 17∘C to 27∘C due to the sunshine. The atmospheric pressure in the room remains 1×10^5 Pa. If ni and nf are the num
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The temperature of an open room of volume ( 30 mathrm{m} ) from ( 17^{circ} mathrm{C} ) to ( 27^{circ} mathrm{C} ) due to the sunshine. The atmospheric pressure in the room remains ( 1 times 10^{5} ) 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
(a) ( 1.38 times 10^{23} )
(b) ( 2.5 times 10^{25} )
( (c)-2.5 times 10^{25} )
(d) ( -161 times 10^{23} )

JEE/Engineering Exams
Physics
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The temperature of an open room of volume 30m from 17∘C to 27∘C due to the sunshine. The atmospheric pressure in the room remains 1×10^5 Pa. If ni and nf are the number of molecules in the room before and after heating, then n_f−n_i will be
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From ( p V=n R T=frac{N}{N_{A}} R T )
We have, ( n_{f}-n_{i}=frac{p V N_{A}}{R T_{f}}-frac{p V N_{A}}{R T_{i}} )
( Rightarrow n_{f}-n_{i}=frac{10^{5} times 30}{8.3} times 6.02 times 10^{23} cdotleft(frac{1}{300}-frac{1}{290}right) )

( =-2.5 times 10^{25} )
(Δn =-2.5 times 10^{25} )

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