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Question
Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?
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Solution
For two states to be connected by an isothermal process,
P1V1 = P2V2 ... (i)
For the same two states to be connected by an adiabatic process,
P1V1γ = P2V2γ ...(ii)
If both the equations hold simultaneously then, on dividing eqaution (ii) by (i) we get
V1γ-1 = V2γ-1
Let the gas be monatomic. Then,
γ =`5/3`
`=> "V"_1^ (2/3)= "V"_2^(2/3)`
⇒ V1 = V2
If this condition is met, then the two states can be connected by an isothermal as well as an adiabatic process.
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