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Question: For a gas having molar mass M, specific heat at constant pressure per gm of gas is given by...

For a gas having molar mass M, specific heat at constant pressure per gm of gas is given by

A

γRM(γ−1)\frac{\gamma R}{M(\gamma - 1)}

B

γRM\frac{\gamma}{RM}

C

MR(γ−1)\frac{M}{R(\gamma - 1)}

D

γRM(γ+1)\frac{\gamma RM}{(\gamma + 1)}

Answer

γRM(γ−1)\frac{\gamma R}{M(\gamma - 1)}

Explanation

Solution

Cp – Cv = Rand CpCv\frac{C_{p}}{C_{v}} = g

\ Cp – Cpγ\frac{C_{p}}{\gamma} = R

or Cp (γ−1γ)\left( \frac{\gamma - 1}{\gamma} \right)= R

or Cp = Rγ(γ−1)\frac{R\gamma}{(\gamma - 1)}= M C‾p{\overline{C}}_{p}

or C‾p{\overline{C}}_{p} = γRM(γ−1)\frac{\gamma R}{M(\gamma - 1)}