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Chapter 2: Q72P (page 542)

A long, closed cylindrical tank contains a diatomic gas that is maintained at a uniform temperature that can be varied. When you measure the speed of sound v in the gas as a function of the temperature T of the gas, you obtain these results:

(a) Explain how you can plot these results so that the graph will be well fit by a straight line. Construct this graph and verify that the plotted points do lie close to a straight line. (b) Because the gas is diatomic, g = 1.40. Use the slope of the line in part (a) to calculate M, the molar mass of the gas. Express M in grams/mole. What type of gas is in the tank?

Short Answer

Expert verified

A) The equation that states the straight line of the graph is v2=纬搁MT

B)M=46.5g/mol

Step by step solution

01

Relation between the speed of sound v and the temperature T

The speed of sound v and the temperature T is v=纬RTMwhere 纬is the ratio of heat capacities, M is the molar mass and R is gas constant

02

Graph between v and T

Take the square of both sides of the above equation, so we can plot a graph between v and T

v2=纬搁MT

Plot a graph between v2and T. As shown in the figure below, the graph is a straight line.

03

Calculate the slope of the graph

The slope of the graph is 纬搁MFor the diatomic gas 纬=1and R=8.314J/mol.kNow, we find the slope from the curve and solve the equation for M

Slope=14*104m2/s2-13.5m2/s340K-320K=250m2/Ks2M=1.40脳8.3114J/molK250m2/Ks2=0.0465Kg/mol=46.5g/mol

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