Calculating Entropy Change in a Lead-Lake System

[Chemmjr18]

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).

 

[Chestermiller]

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?

 

[Chemmjr18]

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.

 

[Chestermiller]

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.

 

[Chemmjr18]

Confirmed.

Thanks for the help!