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Calculate the speed of sound at 288 K in hydrogen, helium, and nitrogen. Under what conditions will the speed of sound in hydrogen be equal to that in helium?

1 Answer

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Step-by-step explanation:

The sped of sound is given as follows.

C =
√(\gamma RT)

It is known that for hydrogen,

R = 4124 J/kg K

T = 288 k


\gamma = 1.41

Therefore, calculate the value of
C_(hydrogen) as follows.


C_(hydrogen) = √(\gamma RT)

=
√(1.41 * 4124 J/kg K * 288)

= 1294.1 m/s

For helium,

R = 2077 J/kg K

T = 288 k


\gamma = 1.66

Therefore, calculate the value of
C_(helium) as follows.


C_(helium) = √(\gamma RT)

=
√(1.66 * 2077 J/kg K * 288)

= 996.48 m/s

For nitrogen,

R = 296.8 J/kg K

T = 288 k


\gamma = 1.4

Therefore, calculate the value of
C_(hydrogen) as follows.


C_(hydrogen) = √(\gamma RT)

=
√(1.4 * 296.8 J/kg K * 288)

= 345.93 m/s

So, speed of sound in hydrogen is calculated as follows.

=
\sqrt{1.41 * 4124 * T_(H)}

=
76.26 \sqrt{T_(H)}

Speed of sound in helium is as follows.

=
\sqrt{1.66 * 2077 * T_(He)}

=
58.72 \sqrt{T_(He)}

For both the speeds to be equal,


76.26 \sqrt{T_(H)} =
58.72 \sqrt{T_(He)}


(T_(H))/(T_(He)) = 0.593

Therefore, we can conclude that the temperature of hydrogen is 0.593 times the temperature of helium.

User SNeumann
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