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A gas undergoes an adiabatic process in ...

A gas undergoes an adiabatic process in which pressure becomes `((8)/(3 sqrt(3)))` times and volume becomes `(3)/(4)` of initial volume. If initial absolute temperature was `T` , the final temperature is

A

`(32T)/(9sqrt(3))`

B

`(2T)/(sqrt(3))`

C

`T^(3/2)`

D

`(sqrt(3)T)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
For adiabatic process `P_(1)V_(1)^(gamma) = P_(2)V_(2)^(gamma) implies P_(0)V_(0)^(gamma) = ((8)/(3sqrt(3))P_(0)) ((3)/(4)V_(0))^(gamma)` `(" …")` (i)
Also , `T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1) = implies TV_(0)^(gamma-1) = T_(2)((3)/(4)V_(0))^(gamma-1)` `( .....)` (ii) Solving (i) &(ii) , `T_(2) = (2T)/(sqrt(3))`
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