Question 400: Thermodynamics & KTG

Question

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 $ 	imes $ 10
–8
s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

Accepted Answer

t $ \propto $ ${{Volume} \over {velocity}}$
volume $ \propto $ ${T \over P}$
$ 	herefore $  t $ \propto $ ${{\sqrt T } \over P}$
${{{t_1}} \over {6 	imes {{10}^{ - 8}}}} = {{\sqrt {500} } \over {2P}} 	imes {P \over {\sqrt {300} }}$
t
1
= 3.8 $ 	imes $ 10
$-$8
$ \approx $  4 $ 	imes $ 10
$-$8

Answer

0.5 $ 	imes $ 10
$-$8
s

Answer

4 $ 	imes $ 10
$-$8
s

Answer

3 $ 	imes $ 10
$-$6
s

Answer

2 $ 	imes $ 10
$-$7
s

Thermodynamics & KTG

An ideal gas is enclosed in a cylinder at pressure of 2 atm and temperature 300 K. The mean time between two successive collisions is 6 \times 10 –8 s. If the pressure is doubled and temperature is increased to 500 K, the mean time between two successive collisions will be close to

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