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When volume of a system is increased two...

When volume of a system is increased two times and temperature is decreased to half of its initial temperature, then pressure becomes

A

2 times

B

4 times

C

`(1)/(4)` times

D

`(1)/(2)` times

Text Solution

Verified by Experts

The correct Answer is:
C
As, ` rho V = RT `
`rArr rho_(1) V_(1) = RT_(1) and V_(2) = 2V_(1) , T_(2) = (T_(1))/(2) rho_(2)` = ?
`( rho_(1) V_(1))/( rho_(2) V_(2)) = (T_(1))/( T_(2)) rArr ( rho_(1))/( rho_(2)) > ( V_(1))/( 2 V_(1)) = ( 2T_(1))/( T_(1))`
`rArr ( rho_(1))/( rho_(2)) = 4`
`rho_(2) = ( rho_(1))/( 4)` = One - fourth of initial pressure .
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