Question 928: Thermodynamics & KTG

Question

What is the ratio of the velocity of sound in hydrogen $$\left(\gamma=\frac{7}{5}\right)$$ to that in helium $$\left(\gamma=\frac{5}{3}\right)$$ at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)

Accepted Answer

Velocity of sound is given by
$$V = \sqrt {{{\gamma RT} \over M}} $$ $$\quad$$ $$	herefore$$ $${{{V_H}} \over {{V_{He}}}} = \sqrt {{{{\gamma _H}} \over {{\gamma _{He}}}}\,.\,{{{M_{He}}} \over {{M_H}}}} $$ (T is the same for both)
$$ = \sqrt {{7 \over 5} 	imes {3 \over 5} 	imes {4 \over 2}}  = {{\sqrt {42} } \over 5}$$

Answer

$$\frac{\sqrt{42}}{5}$$

Answer

$$\frac{5}{\sqrt{42}}$$

Answer

$$\frac{\sqrt{21}}{5}$$

Answer

$$\frac{5}{\sqrt{21}}$$

Thermodynamics & KTG

What is the ratio of the velocity of sound in hydrogen $\left(\gamma=\frac{7}{5}\right) to that in helium \left(\gamma=\frac{5}{3}\right)$ at the same temperature? (Molecular weight of hydrogen and helium is 2 and 4 respectively.)

Choose the correct answer: