Question

For a certain gas, Cp = 840.4 J/kg-K; and Cv = 651.5 J/kg-K. How fast will sound travel in this gas if it is at an adiabatic state with a temperature of 377 K.

Answer 1

Sound will travel with a speed of 302.9 m/sec

Step-by-step explanation:

We have given
`c_p=840.4j/kg-K`

And
`c_v=651.5j/kg-K`

Temperature T = 377 K

Gas constant
`R=c_p-c_v=840.4-651.5=188.9j/kg-K`

And
`\gamma =(c_p)/(c_v)=(840.4)/(651.5)=1.289`

Speed is given by
`v=√(\gamma RT)=√(1.289* 188.9* 377)=302.9794m/sec`

So sound will travel with a speed of 302.9 m/sec

Answer 2

The speed of the sound for the adiabatic gas is 313 m/s

Step-by-step explanation:

For adiabatic state gas, the speed of the sound c is calculated by the following expression:

`c=\sqrt(\gamma*R*T)`

Where R is the gas's particular constant defined in terms of Cp and Cv:

`R=Cp-Cv`

For particular values given:

`R=840.4 (J)/(Kg-K)- 651.5 (J)/(Kg-K)`

`R=188.9 (J)/(Kg-K)`

The gamma undimensional constant is also expressed as a function of Cv and Cp:

`\gamma=Cp/Cv`

`\gamma=840.4 (J)/(Kg-K) / 651.5 (J)/(Kg-K)`

`\gamma=1.29`

And the variable T is the temperature in Kelvin. Thus for the known temperature:

`c=\sqrt(1.29*188.9 (J)/(Kg-K)*377 K)`

`c=\sqrt(91867.73 (J)/(Kg))`

The Jules unit can expressing by:

`J=N.m=(Kg.m)/(s^2)* m`

`J=(Kg.m^2)/(s^2)`

Replacing the new units for the speed of the sound:

`c=\sqrt(91867.73 (Kg.m^2)/(Kg.s^2))`

`c=\sqrt(91867.73 (m^2)/(s^2))`

`c=313 m/s`