Question

Helium (density 0.18 kg/m3 at 0°C and 1 atm pressure)

remains a gas until the extraordinarily low temperature of 4.2 K. What is the speed of sound in helium at 5 K?

Short answer

The speed of sound through helium in the given condition is$131.74m/s$.

Step-by-step solution

Formula to be used

Speed of sound in helium can be determined by,

$v=\sqrt{\frac{\gamma RT}{M}}$

$\gamma \to 1.67$(specific heats ratio)

$R\to 8.314atm/mol/K$(Univ. gas constant)

$T\to 5K$(temperature given)

$M\to 4\times {10}^{-3}kg/mole$(Molecular mass of helium)

Determination of speed

The speed of sound in helium at temperature $T=5K$can be determined by,

$$\begin{gathered} v=\sqrt{\frac{\gamma RT}{M}} \\ v=\sqrt{\frac{1.67\times 8.314\times 5}{4\times {10}^{-3}}} \\ v=131.74m/s \end{gathered}$$