Question

A) At a temperature of 27 ?C, what is the speed of longitudinal waves in hydrogen (molar mass 2.02 g/mol)? The ratio of heat capacities for hydrogen is ?=1.41.

Answer:v =

1320

m/s

B) At a temperature of 27 ?C, what is the speed of longitudinal waves in helium (molar mass 4.00 g/mol)? The ratio of heat capacities for helium is ?=1.67.

Answer:v =

1020

m/s

C)

At a temperature of 27 ?C, what is the speed of longitudinal waves in argon (molar mass 39.9 g/mol)? The ratio of heat capacities for argon is ?=1.67.

Answer:v =

323

m/s

D,E, F i need help please and show work please

D)Compare your answer for part A with the speed in air at the same temperature. The ratio of heat capacities for air is ?=1.40.

E)Compare your answer for part B with the speed in air at the same temperature. The ratio of heat capacities for air is ?=1.40.

F)Compare your answer for part C with the speed in air at the same temperature. The ratio of heat capacities for air is ?=1.40.

Answer 1

The formula that gives the speed of longitudinal waves in a medium is

where

= Adiabatic constant or ratio of heat capacities = 1.40

R = Gas Constant = 8.314 J/mol.K

T = Temperature = 27 + 273 = 300 K

M = Molecular Mass = 0.02895 kg/mol for dry air.

Calculating the speed of longitudinal waves in air at 300 K, we get

So, v_wave = 347.3 m/s

D) The speed of the wave in hydrogen has been determined as

v_A = 1320 m/s

Comparing this with the speed of the wave in air, we get

v_A / v_wave = 3.8, which is the square root of the ratio of the molecular masses of air and hydrogen.

The large difference in the molecular masses of the above two is the reason why the speed of the wave is so distinct.

E) The speed of the wave in helium has been determined as

v_B = 1020 m/s

Comparing this with the speed of the wave in air, we get

v_B / v_wave = 2.94.

This is equivalent to

As can be seen the speed of the wave in Helium is much more due to the difference in molecular masses.

F) The speed of the wave in argon has been determined as

v_C = 323 m/s

Comparing this with the speed of the wave in air, we get

v_C / v_wave = 0.93.

This is equivalent to

The molecular mass of argon and air are not as different as those for helium and hydrogen and the difference in adiabatic constants is also responsible for the speeds being different by a small margin in the two media.