Calculating Time Constant Using Slope of ln(Temperature Dimensionless) vs. Time

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SUMMARY

The discussion centers on calculating the time constant (tau) using the slope of the graph of ln(temperature dimensionless) versus time. The slope provided is -0.0416, leading to the equation m = -1/tau. The user successfully determines the time constant as tau = 24.04 seconds by rearranging the equation to tau = -1/slope.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with the concept of time constants in physics
  • Basic knowledge of graph interpretation
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the relationship between slope and time constants in exponential decay
  • Learn about the applications of time constants in thermal dynamics
  • Explore advanced topics in logarithmic functions and their graphical representations
  • Investigate other methods for calculating time constants in different contexts
USEFUL FOR

Students in physics, particularly those studying thermodynamics or kinetics, as well as educators and anyone involved in experimental data analysis related to temperature changes.

jrodmckis
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Given:

slope of the graph of ln(temperature dimensionless) vs. time

slope=-0.0416

-t/tau = ln(temperature dimensionless)

I don't know where to put the slope into the equations?

I know that the time constant is the tau.

Also have -1/tau equation.

I tried this:

-(1/0.0416) = 24.04 sec is this the time constant?
 
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nevermind i figured it out.

m=-1/tau

and the slope is given
 
Moved from General Physics to homework forums.
 

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