Thermodynamics: Object 1 in contact with Object 2

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SUMMARY

The discussion focuses on calculating the final temperature of an aluminum baseball bat after being brought into a warm room. The bat, weighing 1.3 kg with a specific heat capacity of 0.90 kJ/kgK, is initially at 0°C, while the room temperature is 25°C with 76 kg of air having a specific heat capacity of 1.02 kJ/kgK. The key conclusion is that the heat gained by the bat (Qb) equals the heat lost by the room (Qr), allowing for the determination of the final temperature (Tf) to be approximately 23.51°C.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically heat transfer.
  • Familiarity with the specific heat capacity formula: Q = c m (Tf - Ti).
  • Basic algebra skills for solving equations with one unknown.
  • Knowledge of closed system dynamics in thermodynamics.
NEXT STEPS
  • Study the concept of heat transfer in closed systems.
  • Learn about the specific heat capacities of various materials.
  • Explore thermodynamic equilibrium and its applications.
  • Practice solving heat transfer problems using different materials and conditions.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, educators teaching heat transfer concepts, and anyone interested in practical applications of thermal equilibrium in closed systems.

p1mpz0r
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Homework Statement


After some digging, you locate your aluminum baseball bat (1.3 kg, c = 0.90 kJ/KgK) in a snowbank(0 Celsius) and bring it into a warm (25 Celsius) room. If the 64 m^3 room contains 76 kg of air (c = 1.02 kJ/KgK) and no one goes in or out of the (closed) room, what is the temperature of the bat the next day?

Homework Equations


Q = c m (Tf - Ti)

The Attempt at a Solution



Apparently the Q caused by the bat is equal to the Q lost by the room, I'm just not sure how to calculate Qb and Qr (Qb being the Heat of the Bat, and Qr being the heat of the room), given that I don't have a final temperature.

I know it's super simple, but I'd love some clarity on the situation. Thanks!
 
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p1mpz0r said:
Apparently the Q caused by the bat is equal to the Q lost by the room, I'm just not sure how to calculate Qb and Qr (Qb being the Heat of the Bat, and Qr being the heat of the room), given that I don't have a final temperature.
You have to determine Tf. You have all the information to do this.

Write out the equation for the heat flow into the bat (using the form of equation you have stated). That is your first equation. The unknown on the left side is Qb and on the right side the unknown is Tf.

Write out the equation for the heat flow out of the room (again using the same form of equation). That is your second equation. The unknowns are Qr and Tf.

Since, as you have said, the magnitudes of Qb and Qr are equal, you can reduce this to one equation with one unknown, Tf. Solve for Tf.

AM
 
Thank you thank you thank you :]

Turns out to be ~ 23.51 Celsius
 

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