Question 354: Thermodynamics & KTG

Question

Number of molecules in a volume of 4 cm
3
of
a perfect monoatomic gas at some temperature
T and at a pressure of 2 cm of mercury is close
to?
(Given, mean kinetic energy of a molecule
(at T) is 4 $$ 	imes $$ 10
–14
erg, g = 980 cm/s
2
, density of
mercury = 13.6 g/cm
3
)

Accepted Answer

$$E = {3 \over 2}kT \Rightarrow \left( {T = {{2E} \over {3k}}} ight),$$
Also $$\,PV = NkT$$
$$P = ho gh,\,V = 4c{m^3}$$
$$ 	herefore $$ ($$ho gh$$)V = $$Nk 	imes {{2E} \over {3k}}$$
$$ \Rightarrow $$ $$13.6 	imes {10^3} 	imes 9.8 	imes 2 	imes {10^{ - 2}} 	imes 4 	imes {10^{ - 6}}$$
$$ = Nk 	imes {{2E} \over {3k}} = {{N 	imes 2} \over 3} 	imes 4 	imes {10^{ - 14}} 	imes {10^{-7}}$$
$$ \Rightarrow $$ $$N = {{13.6 	imes 19.6 	imes 4 	imes {{10}^{ - 5}} 	imes 3 	imes 10} \over 8}$$
$$ \Rightarrow $$ $$N = 399.84 	imes {10^{16}}$$
$$ = 3.99 	imes {10^{18}}$$
$$ \Rightarrow $$ $$N = 4 	imes {10^{18}}$$

Answer

5.8 $$ 	imes $$ 10
18

Answer

4.0 $$ 	imes $$ 10
16

Answer

5.8 $$ 	imes $$ 10
16

Answer

4.0 $$ 	imes $$ 10
18

Thermodynamics & KTG

Number of molecules in a volume of 4 cm 3 of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is 4 $ \times $ 10 –14 erg, g = 980 cm/s 2 , density of mercury = 13.6 g/cm 3 )

Choose the correct answer: