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  • The molecules of a given mass of gas have the most probable speed of 100 m/s at 270 C and  1.0 X 10 5 N/m2 pressure. When the temperature is 1270 C

The molecules of a given mass of gas have the most probable speed of 100 m/s at 270 C and  1.0 X 10 5 N/m2 pressure. When the temperature is 1270 C and pressure is 0.5 X 105 N/m2 .The most probable speed (in m/sec) of the molecule will be.

Option: 1

230.94


Option: 2

115.47


Option: 3

200


Option: 4

250


Answers (1)

best_answer

As we learned

Most probable speed of a molecule of a gas -

V_{mp}= \sqrt{\frac{2KT}{m}}

= \sqrt{\frac{2RT}{M}}

- wherein

K = Boltzmann's Constant

m = mass of a molecule

M = molar mass

R = Universal gas constant

T = Temperature

 

 1363

 

Most probable speed

V_{mp}= \sqrt{\frac{2p}{\phi }}= \sqrt{\frac{2RT}{M}}= \sqrt{\frac{2KT}{m}}

Most probable speed does not depend upon pressure it depend upon temperature.

V_{mp}\alpha \sqrt{T}

\frac{v_{1}}{v_{2}}= \frac{T_{1}}{T_{2}}= \sqrt{\frac{273+27}{273+127}}

\frac{v_{1}}{v_{2}}= \sqrt{\frac{300}{400}}\Rightarrow \\*\frac{100}{v_{2}}= \sqrt{\frac{3}{4}}\Rightarrow v_{2}= \frac{200}{\sqrt{3}}\: m/s

Posted by

Divya Prakash Singh

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