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A diatomic gas initially at 18^(@) is co...

A diatomic gas initially at `18^(@)` is compressed adiabatically to one- eighth of its original volume. The temperature after compression will b

A

` 395 ,4""^(@)C `

B

` 144 ""^(@) C`

C

` 18^(@) C `

D

` 887.4^(@)C `

Text Solution

Verified by Experts

The correct Answer is:
A
Initial temperature ` (T_1) = 18^(@) C`
`=( 273 +18) =291 K and V_2= V_1//8.`
For adiabatic compression , ` TV^(gamma -1) = ` constant
OR ` T_1V_1^(gamma -1) = T_2 V_2^(gamma -1)`
Therefore ` T_2= T_1((V_1)/(V_2))^(gamma-1)`
`= 291 xx (8) ^(1.4-1)= 291 xx (8)^(0.4)`
` 291 xx 2.297 = 668 .4 K = 395 .4^(@) C `
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