Entropy change as mass tends to infinity

Q/T (subscript i). The formula for change in entropy is mc ln (Tf/Ti), where Tf and Ti are the final and initial temperatures respectively. However, as the mass tends to infinity, the expression for change in entropy can become unbounded.
  • #1

blueyellow

'show that the entropy change of the object tends towards deltaQ/T (subcript i) as its mass tends to infinity, in the4 limit where it becomes a heat bath

i got:
change in entropy =mc ln (Tf/Ti) (mc ln (T subcript f/T subcript i))

but if the mass tends to inifinity the expression seems to blow up

thanks in advance
 
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  • #2
blueyellow said:
'show that the entropy change of the object tends towards deltaQ/T (subcript i) as its mass tends to infinity, in the4 limit where it becomes a heat bath

i got:
change in entropy =mc ln (Tf/Ti) (mc ln (T subcript f/T subcript i))

but if the mass tends to inifinity the expression seems to blow up

thanks in advance
As the mass increases what happens to Tf/Ti?

Let Tf = Ti + dT where Ti is very close to Tf.

Express the change in entropy in terms of Ti and dT.

AM
 

1. What is entropy change as mass tends to infinity?

Entropy change as mass tends to infinity refers to the change in the level of disorder or randomness in a system as the mass of the system increases towards infinity. It is a concept in thermodynamics that describes the relationship between entropy and mass.

2. Why is entropy change important in relation to mass increasing towards infinity?

Entropy change is important in this context because it helps us understand the behavior of systems with a large number of particles. As the mass of a system increases towards infinity, the number of particles also increases, leading to a higher degree of disorder and randomness in the system. This has implications on the overall stability and predictability of the system.

3. How does entropy change as mass tends to infinity relate to the second law of thermodynamics?

The second law of thermodynamics states that the total entropy of a closed system will always increase over time. As the mass of a system tends to infinity, the number of particles in the system also increases, leading to a higher entropy. This is in line with the second law of thermodynamics, as the overall disorder and randomness in the system increases with a larger number of particles.

4. Can entropy change as mass tends to infinity be reversed?

No, entropy change as mass tends to infinity cannot be reversed. According to the second law of thermodynamics, the overall entropy of a system will always increase over time. Even if a system with a large mass is artificially brought back to a state of lower entropy, the overall trend will still be towards an increase in entropy.

5. How is entropy change as mass tends to infinity measured?

Entropy change as mass tends to infinity is measured using the Boltzmann equation, which relates the entropy of a system to its number of possible microstates. As the mass of a system increases towards infinity, the number of microstates also increases, leading to a higher entropy value. Other methods of measuring entropy, such as information theory, can also be used in this context.

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