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Question
Can two states of an ideal gas be connected by an isothermal process as well as an adiabatic process?
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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