The Whistling Tea Kettle · AI Generator #GEN-00FBE9E1
Physics · thermodynamics
Problem
A traditional tea kettle whistles when steam escapes through a small circular opening in its spout. The whistle occurs because the steam jet becomes unstable and oscillates at a frequency determined by the steam's properties.
Consider a kettle where water boils at atmospheric pressure (1.01×105Pa). The steam escapes through a circular hole of diameter d=3.0mm in the spout. The whistle frequency is given by the empirical relation:
f=d0.2v
where v is the average speed of steam molecules and d is the hole diameter.
(a) Calculate the average speed of water vapor molecules at 100°C using kinetic theory.
(b) What is the frequency of the kettle's whistle?
(c) If the kettle is taken to a mountain location where atmospheric pressure is 0.85×105Pa, by what factor does the whistle frequency change? (Assume the boiling point changes to 95°C at this pressure.)
Use: R=8.314J/(mol⋅K), molar mass of water M=18.0g/mol.