Question 439: Thermodynamics & KTG

Question

The temperature of an open room of volume 30 m
3
increases from 17
o
C to 27
o
C due to the sunshine. The atmospheric pressure in the room remains 1 $$ 	imes $$ 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 :

Accepted Answer

Given: Initial temperature T
i
= 17 + 273 = 290 K
Final temperature T
f
= 27 + 273 = 300 K
Atmospheric pressure, P
0
= 1 ÃÂ 10
5
Pa
Volume of room, V
0
= 30 m
3
Difference in number of molecules, N
f
Ã¢ÂÂ N
i
= ?
We know PV = nRT = $${N \over {{N_A}}}$$RT
The number of molecules
N = $${{PV{N_A}} \over {RT}}$$
$$ 	herefore $$ N
f
Ã¢ÂÂ N
i
= $${{{P_0}{V_0}{N_A}} \over R}\left( {{1 \over {{T_f}}} - {1 \over {{T_i}}}} ight)$$
= $${{1 	imes {{10}^5} 	imes 30 	imes 6.023 	imes {{10}^{23}}} \over {8.314}}\left( {{1 \over {300}} - {1 \over {290}}} ight)$$
= Ã¢ÂÂ 2.5 $$ 	imes $$ 10
25

Answer

- 1.61 $$ 	imes $$ 10
23

Answer

1.38 $$ 	imes $$ 10
23

Answer

2.5 $$ 	imes $$ 10
25

Answer

- 2.5 $$ 	imes $$ 10
25

Thermodynamics & KTG

The temperature of an open room of volume 30 m 3 increases from 17 o C to 27 o 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 :

Choose the correct answer: