A mercury thermometer having a time constant of 0.1 min is placed in a temperature bath of 100°c
Answers
The complete question is,
A mercury thermometer having a time constant of 0.5 min is placed in a temperature bath at 100°F and allowed to come to equilibrium with the bath. At time t=0 , the temperature of the bath begins to vary sinusoidal about its average temperate of 100°F with an amplitude of 4°F. The frequency of oscillation is 10/3π cycles/min. What is the phase lag?
Given:
A mercury thermometer having a time constant of 0.5 min is placed in a temperature bath at 100°F and allowed to come to equilibrium with the bath.
An amplitude of 4°F.
The frequency of oscillation is 10/3π cycles/min.
To find:
What is the phase lag?
Solution:
The phase log formula is given as follows:
∅ = tan^{-1} (-wt)
w = 2πf = 2π × 10/3π = 20/3 rad/min
∅ = tan^{-1} (- 20/3 × 0.5)
= tan^{-1} (- 10/3 )
= - tan^{-1} ( 10/3 )
Phase lag tan^{-1} ( 10/3 )