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. - Physics

Answer in Brief

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 = nC_pdT,
where C_p is the molar heat capacity at constant pressure.
So, 3RndT = nC_pdT
⇒ C_p = 3R