Question

Calculate the speed of sound in oxygen from the following data. The mass of 22.4 litre of oxygen at STP $(T=273KandP=1.0\times {10}^{5}N{m}^{-2})$ is 32g, the molar heat capacity of oxygen at constant volume is $C_V$ = 2.5 R and that at constant pressure is Cp = 3.5 R.

• A. $300\frac{m}{s}$
• B. $315\frac{m}{s}$
• C. $350\frac{m}{s}$
• D. $365\frac{m}{s}$

Answer 1

The correct option is B $315\frac{m}{s}$

The mass of 22.4 L of any ideal gas at STP = molecular mass.

Considering oxygen to be ideal

M${}_{Oxygen}$ = 32 g

C${}_V$ = 2.5 R, C${}_P$ = 3.5 R (given)

V${}_1$ speed of sound in

$O_2=\sqrt{\frac{\gamma RT}{M}}$

$\sqrt{\frac{\left(\frac{C_P}{C_V}\right).R.273}{32\times {10}^{-3}}}$

$=315\frac{m}{s}$