Solving for Entropy Change: Copper & Water

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SUMMARY

The discussion focuses on calculating the entropy change of a system consisting of a 500 g copper block at 80°C and 1.0 kg of water at 10°C. The final equilibrium temperature is determined to be 290 K using the formula T_f = (m1*c1*T1 + m2*c2*T2) / (m1*c1 + m2*c2). To find the entropy change, the equation ΔS = ∫(dQ/T) is utilized, where dQ is defined as m·c·dT. The total entropy change is the sum of the entropy changes for both the copper and water systems, ensuring that the total change is greater than or equal to zero.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically entropy.
  • Familiarity with heat transfer equations, particularly dQ = m·c·dT.
  • Knowledge of equilibrium temperature calculations using specific heat capacities.
  • Basic calculus for integrating functions in the context of thermodynamic equations.
NEXT STEPS
  • Study the derivation and application of the entropy formula ΔS = ∫(dQ/T).
  • Learn about specific heat capacities of different materials, focusing on copper and water.
  • Explore the laws of thermodynamics, particularly the second law regarding entropy.
  • Practice problems involving entropy changes in various thermodynamic systems.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, physics educators, and anyone interested in understanding entropy changes in thermal systems involving metals and liquids.

MeliMo
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Homework Statement


A 500 g copper block at 80 C is dropped into 1.0 kg of water at 10 C. Find the entropy change of the system.


Homework Equations


dS= integral of dQ/T


The Attempt at a Solution


I found that the final equilibrium temperature is 290 K using the equation
[(m1*c1*dT1) + (m2*c2*dT2)]/ [(m1*c1) + (m2*c2)]
I know that this is correct, but I'm not sure what to do from here. I know that this is Tf, but what do I use as Ti for the integral, the temperature of the block or the water? And which equation do I integrate to find the entropy in this case (What is the equation for Q)?
 
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Well, not sure why you wrote dT1 and dT2 in the equation. But you are correct if you meant:
T_f = \left(m_1 c_1 T_1 + m_2 c_2 T_2\right)/\left(m_1 c_1 + m_2 c_2\right)

You also know that dQ = m\cdot c\cdot dT but forgot to mention it in your list of equations. Knowing this and that
\Delta S = \int_{T_i}^{T_f}dQ/T
you can solve for the change in entropy, \Delta S, for both systems. The total change in entropy will just be the sum of the two values.

P.S.: Be careful with units. And be sure the total change in entropy is greater than or equal to zero, we don't want to be breaking any laws here :)
 


Thank You!
 

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