Solve Temperature Problem: 8.7 Deg C

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SUMMARY

The discussion centers on calculating the final temperature of a system involving a glass of water and condensation. The initial conditions include a 122 gm glass with 222 gm of water at 5.0°C, with 4.5 gm of water condensing on the glass. The correct final temperature is determined to be 14.9°C through the application of heat energy equations, specifically Q = mCΔT for the glass and water, and Q = mL for the condensation. The calculations reveal that the total heat energy before condensation is 1232 cal, and the heat released during condensation is 2430 cal, leading to the final temperature calculation.

PREREQUISITES
  • Understanding of heat transfer principles, specifically Q = mCΔT and Q = mL.
  • Knowledge of specific heat capacities for water and glass.
  • Ability to perform basic algebraic manipulations to solve for unknowns.
  • Familiarity with the concept of latent heat of condensation.
NEXT STEPS
  • Study the principles of thermodynamics, focusing on heat transfer and energy conservation.
  • Learn about specific heat capacities of various materials, particularly water and glass.
  • Explore the concept of latent heat and its applications in phase changes.
  • Practice solving problems involving heat transfer in mixed systems with varying masses and temperatures.
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Students in physics or chemistry, educators teaching thermodynamics, and professionals involved in thermal management or engineering applications will benefit from this discussion.

Kcoats
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:confused:

The formation of condensation on a cold glass of water will cause it to warm up faster than it would have otherwise. If 4.5 gm of water condenses on a 122 gm glass containing 222 gm of water at 5.0 deg C, what will the final temperature be? Ignore the effect of the surroundings.

The answer for this is 14.9 deg C

But...I can't figure out how to get that answer. lol

Here is what I am doing, where do I go wrong?

(1 cal/g deg C)(222g)(Tf-5 degC) + (.2 cal/g deg C)(122g) (Tf-5 deg C)
(122cal/ deg C)(Tf-5 deg C) + (24.4 cal/deg C)(Tf-5 deg C)
(540 cal/g)=(146.4 cal/ deg C)(Tf-5 deg C)
/146.4 cal/ deg C
3.7=(Tf-5 deg C)
8.7=Tf
 
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Trial and error. :)
I figured out how to work it.

Q=(4.5g)(540cal/g deg C)=2430 cal
(1 cal/g deg C)(222g)(Tf-5 degC) + (.2 cal/g deg C)(122g) (Tf-5 deg C)
(122cal/ deg C)(Tf-5 deg C) + (24.4 cal/deg C)(Tf-5 deg C)=246.4 cal/ deg c(tf-5 deg C)
2430 cal/246.4 cal/deg c=14.9 deg C
 


It seems like you are on the right track, but there are a few mistakes in your calculations. Let's break it down step by step:

1. First, we need to calculate the total heat energy of the system before the condensation occurs. This can be done using the formula Q = mCΔT, where Q is the heat energy, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.

For the glass, we have:
Q1 = (122g)(0.2 cal/g·°C)(5°C) = 122 cal

For the water, we have:
Q2 = (222g)(1 cal/g·°C)(5°C) = 1110 cal

The total heat energy before condensation is:
Qt = Q1 + Q2 = 122 cal + 1110 cal = 1232 cal

2. Next, we need to calculate the heat energy released during the condensation. This can be done using the formula Q = mL, where Q is the heat energy, m is the mass, and L is the latent heat of condensation.

For water, we have:
Q3 = (4.5g)(540 cal/g) = 2430 cal

3. Now, we can calculate the final temperature using the formula Qt = Q1 + Q2 + Q3:
1232 cal = (122g)(0.2 cal/g·°C)(Tf - 5°C) + (222g)(1 cal/g·°C)(Tf - 5°C) + (4.5g)(540 cal/g)
1232 cal = (24.4 cal/°C)(Tf - 5°C) + (222 cal/°C)(Tf - 5°C) + 2430 cal
1232 cal = (246.4 cal/°C)(Tf - 5°C) + 2430 cal
(1232 cal - 2430 cal) = (246.4 cal/°C)(Tf - 5°C)
-1198 cal = (246.4 cal/°C)(Tf - 5°C)
-1198 cal / 246.4 cal/°C = Tf - 5°C
-4.86°C = Tf - 5°C
Tf = 0.14°C

So, the final temperature
 

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