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Write the expressions for Cv and Cp of ...

Write the expressions for `C_v and C_p` of a gas in terms of gas constant R and `gamma` where
`gamma = C_p//C_v`

Text Solution

AI Generated Solution

To derive the expressions for \( C_v \) and \( C_p \) of a gas in terms of the gas constant \( R \) and \( \gamma \) (where \( \gamma = \frac{C_p}{C_v} \)), we can follow these steps: ### Step 1: Understand the relationship between \( C_p \), \( C_v \), and \( R \) We know two important relationships: 1. The ratio of specific heats: \[ \gamma = \frac{C_p}{C_v} \] ...
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A gas undergoes cyclic process 1-2-3-4-1 in which 1-2 and 3-4 are adiabatic process 2-3 and 4-1 are isobaric process. If (P_(2))/(P_(1))=k then what will be the efficiency of cycle in terms of k and gamma where gamma=C_(p)//C_(v) .

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Knowledge Check

  • if R is the molar gas constant and gamma=C_(P)//C_(V), then C_(V) is equal to

    A
    `R//gamma`
    B
    `gammaR`
    C
    `(2R)/(gamma-1)`
    D
    `(R)/(gamma-1)`

  • If R is the molar gas constant and gamma=C_(P)//C_(V), then C_(p) is equal to

    A
    `R//gamma`
    B
    `gammaR`
    C
    `(2R)/(gamma-1)`
    D
    `(Rgamma)/(gamma-1)`

  • For adiabatic processes (gamma = (C_(p))/(C_(v)))

    A
    `P^(gamma) V = constant`
    B
    `T^(gamma) V = constant`
    C
    `T V^(gamma-1) = constant`
    D
    `T V^(gamma) = constant`

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    105 calories of heat is required to raise the temperature of 3 moles of an ideaol gas at constant pressure from 30^(@)C to 35^(@)C. The amount of heat required in calories to raise the temperature of the gas though the range (60 ^(@)C to 65^(@)C) at constant volume is (gamma = (C_(p))/( C_(v)) = 1.4)

    In previous, Find the value of gamma = C_(P) // C_(v) :

    The molar specific heat of an ideal gas at constant pressure and constant volume is C_(p) and C_(v) respectively. If R is the universal gas constant and the ratio of C_(p) to C_(v) is gamma , then C_(v) .

    During an adiabatic process , the pressure p of a fixed mass of an ideal gas change by Deltap and its volume V change by DeltaV . If gamma=C_(p)//C_(v) then DeltaV//V is given by

    The internal energy of a gas is given by U = 3 pV. It expands from V_(0) to 2V_(0) against a constant pressure p_(0) . What is the value of gamma(=C_(P)//C_(V)) for the given gas?

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