Calculating Entropy Change in a Lead-Lake System

In summary, the conversation discusses the determination of entropy change for a 5.0-kg piece of lead placed in a lake with a temperature of 15 Celsius. The entropy change for the lead is calculated using its mass, heat capacity, and initial and final temperatures. The entropy change for the lake and the universe are also considered, with the final values being -710 J/K for the lead, 1300 J/K for the lake, and 590 J/K for the universe. It is noted that the book's answer for the entropy change of the lead may be incorrect.
  • #1
Chemmjr18
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1

Homework Statement



A 5.0-kg piece of lead at a temperature of is 600 Celsius placed in a lake whose temperature is 15 Celsius. Determine the entropy change of (a) the lead piece, (b) the lake, and (c) the universe.

mass of lead=5 kg
initial temperature of lead=873.15 K
final temperature of lead=288.15 assumed that the temperature of lake won't noticeably change)
heat capacity of lead=128 J/(kg⋅K)

Homework Equations


For the lead,
ΔS=mass of lead⋅heat capacity of lead⋅ln(final temperature/initial temperature)

For the lake and the universe I am not sure where to begin.

The Attempt at a Solution


For the lead I got
ΔS=-710 J/K

The books answer is ΔS=-540 J/K for the lead. I feel like the book isn't giving all of the necessary data to solve this problem (i.e. the size of the lake).
 
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  • #2
Chemmjr18 said:

Homework Statement



A 5.0-kg piece of lead at a temperature of is 600 Celsius placed in a lake whose temperature is 15 Celsius. Determine the entropy change of (a) the lead piece, (b) the lake, and (c) the universe.

mass of lead=5 kg
initial temperature of lead=873.15 K
final temperature of lead=288.15 assumed that the temperature of lake won't noticeably change)
heat capacity of lead=128 J/(kg⋅K)

Homework Equations


For the lead,
ΔS=mass of lead⋅heat capacity of lead⋅ln(final temperature/initial temperature)

For the lake and the universe I am not sure where to begin.

The Attempt at a Solution


For the lead I got
ΔS=-710 J/K

The books answer is ΔS=-540 J/K for the lead. I feel like the book isn't giving all of the necessary data to solve this problem (i.e. the size of the lake).
I confirm your 710 value.

How much heat is transferred to the lake? With this amount of heat transferred, if the lake is considered an ideal reservoir at 15 C, what is its change in entropy? What is the sum of the entropy change of the lead and the lake?
 
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  • #3
Chestermiller said:
I confirm your 710 value.

How much heat is transferred to the lake? With this amount of heat transferred, if the lake is considered an ideal reservoir at 15 C, what is its change in entropy? What is the sum of the entropy change of the lead and the lake?

Thanks for your help. I guess the book is wrong (which isn't surprising). For the lake, I got ΔS=1300 J/K and for the universe, I got ΔS=590 J/K.
 
  • #4
Chemmjr18 said:
Thanks for your help. I guess the book is wrong (which isn't surprising). For the lake, I got ΔS=1300 J/K and for the universe, I got ΔS=590 J/K.
Confirmed.
 
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  • #5
Chestermiller said:
Confirmed.
Thanks for the help!
 

1. What is entropy change?

Entropy change is a measure of the amount of disorder or randomness in a system. It is a thermodynamic property that describes the tendency of a system to move towards a state of maximum disorder.

2. How is entropy change calculated?

The change in entropy is calculated by taking the difference between the entropy of the final state and the entropy of the initial state. This can be represented by the equation ΔS = Sf - Si, where ΔS is the change in entropy, Sf is the final entropy and Si is the initial entropy.

3. What factors affect entropy change?

The factors that affect entropy change include temperature, pressure, and the number of particles in a system. Higher temperatures and pressures generally lead to an increase in entropy, while a larger number of particles in a system can also increase entropy.

4. How does entropy change relate to the laws of thermodynamics?

Entropy change is related to the second law of thermodynamics, which states that the total entropy of an isolated system will always increase over time. This means that in any natural process, the total entropy of the system and its surroundings will increase.

5. Why is finding entropy change important in science?

Finding entropy change is important in science because it helps us understand and predict the behavior of systems. It is a fundamental concept in thermodynamics and is used in a wide range of fields, including chemistry, physics, and engineering, to study and design processes and systems.

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