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An ideal gas at 27^(@)C is compressed ad...

An ideal gas at `27^(@)C` is compressed adiabatically to `8//27` of its original volume. If `gamma = 5//3`, then the rise in temperature is

A

450 K

B

375 K

C

225 K

D

405 K

Text Solution

Verified by Experts

The correct Answer is:
B
As `TV^(gamma-1)` = constant
`implies T_2=T_1((V_1)/(V_2))^(gamma-1) implies T_2 =300((27)/(8))^(5/3-1) = 300((27)/(8))^(2/3)`
`implies T_2=300(3/2)^2=300 xx 9/4 = 675 K`
Now change in temperature
`Delta T=675-300=375 K`
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