Question

A monoatomic gas is compressed adiabatically to `(8)/(27)` of its initial volume if initial temperature is `27^@C`, find increase in temperature

Answer 1

`r=(5)/(3)`,`V_1=V_0`,`V_2o=(8)/(27)V_0`,`T_1=27^@C=27+273=300K`
For adiabatic process
`TV^(gamma-1)=`constant
`T_1V_1^(gamma-1)=T_2V_2^(gamma-1)`
`T_2=T_1((V_1)/(V_2))^(gamma-1)=300((V_0)/((8)/(27)V_0))^((5)/(3)-1)`
`=300((27)/(8))^((2)/(3))=(300xx9)/(4)=675K`
`DeltaT=T_2-T_1=675-300`
`=375K=375^@C`