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
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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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