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Question
An amount Q of heat is added to a monatomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding. Find the molar heat capacity for the process
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Solution
Given:
Amount of heat given to the gas = Q
So, ∆Q = Q
Work done by the gas, Δ W = `Q/2`
From the first law of thermodynamics,
ΔQ = ΔW +Δ U
`=> triangle "U" = "Q" - "Q"/2 = "Q"/2`
For a monoatomic gas,
`triangle "U"= 3/2 "n""R""d""T"`
`=> "Q"/2 = "n""d""T" xx3/2 "R"`
⇒ Q = 3nRdT
Again, for expansion at constant pressure,
Q = nCpdT,
where Cp is the molar heat capacity at constant pressure.
So, 3RndT = nCpdT
⇒ Cp = 3R
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