Problem on work done in thermodynamics

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SUMMARY

The discussion focuses on a thermodynamics problem involving a paddle that turns at 28.0 rad/s and exerts a torque of 16.0 Nm to stir paint. The internal energy increase of 12.5 kJ results in a temperature rise of 1.00 K. The key equation utilized is the first law of thermodynamics, represented as Delta U = Q + Wd. The challenge presented is to determine the change in temperature of the paint after 5 minutes of stirring, assuming no heat flow to the surroundings.

PREREQUISITES
  • Understanding of the first law of thermodynamics
  • Familiarity with torque and angular velocity concepts
  • Knowledge of power calculations in mechanical systems
  • Basic principles of internal energy and temperature change
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  • Learn how to calculate energy transfer over time using power equations
  • Explore the implications of the first law of thermodynamics in practical applications
  • Investigate specific heat capacity and its role in temperature change calculations
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Homework Statement


A paddle turns at 28.0 rad/s and exerts a torque of 16.0 Nm to stir the paint.
Internal energy increase of 12.5kJ causes the temperature of the paint to increase by 1.00K.
If there where no heat flow between the paint and the surroundings, what is the change in temperature as it is stirred for 5mins?


Homework Equations


Change of Internal energy, Delta U = Q * Wd
(first law of thermodynamics)

The Attempt at a Solution


I do not know how to start nor attempt...
 
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Is there an equation that relates power, torque, and angular velocity?

They tell you how much energy is needed to raise the temperature of the paint 1 K.

If we can figure the power input, then we can figure the energy added in 5 minutes (think of definition of power).
 

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