Question # 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

# 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} )

Solution

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} )