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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