Answer:
The speed of the sound for the adiabatic gas is 313 m/s
Explanation:
For adiabatic state gas, the speed of the sound c is calculated by the following expression:
[tex]c=\sqrt(\gamma*R*T)[/tex]
Where R is the gas's particular constant defined in terms of Cp and Cv:
[tex]R=Cp-Cv[/tex]
For particular values given:
[tex]R=840.4 \frac{J}{Kg-K}- 651.5 \frac{J}{Kg-K}[/tex]
[tex]R=188.9 \frac{J}{Kg-K}[/tex]
The gamma undimensional constant is also expressed as a function of Cv and Cp:
[tex]\gamma=Cp/Cv[/tex]
[tex]\gamma=840.4 \frac{J}{Kg-K} / 651.5 \frac{J}{Kg-K} [/tex]
[tex]\gamma=1.29 [/tex]
And the variable T is the temperature in Kelvin. Thus for the known temperature:
[tex]c=\sqrt(1.29*188.9 \frac{J}{Kg-K}*377 K)[/tex]
[tex]c=\sqrt(91867.73 \frac{J}{Kg})[/tex]
The Jules unit can expressing by:
[tex]J=N.m=\frac{Kg.m}{s^2}* m[/tex]
[tex]J=\frac{Kg.m^2}{s^2}[/tex]
Replacing the new units for the speed of the sound:
[tex]c=\sqrt(91867.73 \frac{Kg.m^2}{Kg.s^2})[/tex]
[tex]c=\sqrt(91867.73 \frac{m^2}{s^2})[/tex]
[tex]c=313 m/s[/tex]
Answer:
Sound will travel with a speed of 302.9 m/sec
Explanation:
We have given [tex]c_p=840.4j/kg-K[/tex]
And [tex]c_v=651.5j/kg-K[/tex]
Temperature T = 377 K
Gas constant [tex]R=c_p-c_v=840.4-651.5=188.9j/kg-K[/tex]
And [tex]\gamma =\frac{c_p}{c_v}=\frac{840.4}{651.5}=1.289[/tex]
Speed is given by [tex]v=\sqrt{\gamma RT}=\sqrt{1.289\times 188.9\times 377}=302.9794m/sec[/tex]
So sound will travel with a speed of 302.9 m/sec
