Speed of sound in an ideal gas

[espen180]

Homework Statement

Determine the speed of sound in argon gas at 30 degrees celcius. Argon is a monoatomic gas with atomic mass 40. Assume adiabatic and ideal gas conditions. The mass of a nucleuon is 1.67*10^-27 kg=m_p.

Homework Equations

Adiabatic constraint: pV^γ=constant.

Ideal gas equation: pV=nRT=NkT

Speed of a sound wave: $v=\sqrt{B/\rho}$

The Attempt at a Solution

From the adiabatic constraint: $\text{d}p V^{\gamma} + \gamma p V^{\gamma-1} \text{d}V=0$

$B=-V\frac{\text{d}p}{\text{d}V}=\gamma p$

Insert into ideal gas equation, using $\rho=\frac{Nm}{V}$ :

$B=\frac{\gamma \rho k T}{m}$

Finally: $v=\sqrt{\frac{B}{\rho}}=\sqrt{\frac{\gamma k T}{m}}$

Insert values: m=40*m_p=6,68*10^-26 kg, k=1.38*10^-23 J/K, T=303.15 K, γ=3/5=0.6

This produces the result v=194 m/s.

However, the answer key says the correct value is 323 m/s

I have searched my solution attempt multiple times, unable to find my error. Any help will be greatly appreciated.

 

[ehild]

Insert values: m=40*m_p=6,68*10^-26 kg, k=1.38*10^-23 J/K, T=303.15 K, γ=3/5=0.6

γ=C_p/C_v=5/3 for a mono-atomic gas.


ehild

 

[espen180]

Thank you. What an embarrasing mistake.