Problem on entropy change and specific heat capacity

In summary, the change in entropy of the Universe can be calculated by finding the entropy change of the copper block and the lake separately and then adding them together. This can be done by using the equations dS=dQ/T and dQ=mCdT, and integrating between the boundaries of the temperatures. There was a typo in the given information, but after adjusting for it, the problem becomes simpler and the total change in entropy can be easily calculated.
  • #1
con31773
6
0
Calculate the change in entropy of the Universe as a result of the following
operations:
(a) A copper block of mass 0.4kg and thermal capacity 150JK-1 at 100◦C is
placed in a lake at 10◦C.

dS=dQ/T dQ=mCdT

Tried simply combining these equations and integrating to find change of entropy of block. Knowing that final temperature of the block will be approximately the initial temperature of the lake. So we get
mc[ln(T)] between boundaries of T1 and T2. However, this thermal capacity does not have the standard units for c, which is JK-1Kg-1, so I am questioning my whole approach. Assuming this is just some typo perhaps and I do indeed do this, I am not sure on how to find the universal entropy change. Any help would be greatly appreciated.
Many thanks in advance.
 
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  • #2
It's an obvious typo, so, what is the change in entropy of the block?
How much heat is transferred from the block to the lake?
At what temperature does the lake receive this heat?
What is the change in entropy of the lake?
What is the total change in entropy for the block plus lake?

Chet
 
  • #3
Does it have to be a typo? The 0.4kg could just be a red herring.
 
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  • #4
rude man said:
Does it have to be a typo? The 0.4kg could just be a red herring.
True. Who knows?

Chet
 
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  • #5
It turns out It wasn't a typo, the C here was the heat transfer per unit temperature (multiple of C and M), something I was not familiar with. As a result the the question becomes much simpler, just being the sum of the two entropy change (block and lake)
Your help was much appreciated :)
 

Related to Problem on entropy change and specific heat capacity

1. What is entropy change and why is it important?

Entropy change refers to the measure of the disorder and randomness in a system. It is important because it helps us understand and predict the direction of spontaneous processes and the efficiency of energy conversions.

2. How is entropy change related to specific heat capacity?

Entropy change is related to specific heat capacity because specific heat capacity is a measure of the amount of heat required to change the temperature of a substance. This change in temperature can also affect the degree of disorder and randomness in a system, thus impacting the entropy change.

3. What factors affect the entropy change in a system?

The factors that affect entropy change in a system include temperature, pressure, and the number of particles present. In general, an increase in temperature and pressure leads to an increase in entropy, while a decrease in the number of particles can decrease entropy.

4. Can specific heat capacity be negative?

No, specific heat capacity cannot be negative. It is a physical property of a substance and is always a positive value. However, the change in specific heat capacity (delta C) can be negative, indicating a decrease in the amount of heat required to change the temperature of a substance.

5. How is entropy change calculated?

Entropy change is calculated using the equation delta S = Q/T, where Q is the heat transferred and T is the temperature in Kelvin. The units for entropy change are joules per Kelvin (J/K).

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