Confusion about relation of entropy with temperature.

In summary, the conversation discusses the relationship between entropy and temperature. It is mentioned that in an adiabatic change of state, such as an expansion, the entropy remains constant due to the equation ##\delta Q = T dS##. The equation for the entropy change of an ideal gas is also mentioned, and it is explained that for a change in entropy to be zero, the temperatures must be equal. This is because entropy change can occur due to heat transfer and internal irreversibilities, and the second law states that the entropy change will always be greater than the entropy transferred through heat.
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Engineer1
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Why can sometimes entropy remain constant with increase of temperature and vice versa?Entropy implies transfer of heat and heat must increase with temperature.I am unable to intuitively understand.
 
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With ##\delta Q = T dS## you can see that this happens for an adiabatic (##\delta Q = 0##) change of state, e.g. an expansion. (reversible, because of the ##dS=0##, so an idealization).
 
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You can see why by considering the entropy change for a closed system of an ideal gas (assuming constant specific heats).

##\Delta S = c_p \cdot Ln\frac{T_2}{T_1} + R \cdot Ln\frac{P_2}{P_1}##

So if we ##\Delta S = 0## do you see anything that would require ##T_1 = T_2##? Recall that entropy change may occur due to heat transfer, and internal irreversibilities. The second law requires that for all real processes the entropy change will be larger than the entropy that is transferred along with heat.
 
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1. What is the relation between entropy and temperature?

The relationship between entropy and temperature is known as the Second Law of Thermodynamics. It states that as the temperature of a system increases, the entropy of the system also increases. This means that as a system gets hotter, the amount of disorder or randomness within the system also increases.

2. How does temperature affect entropy?

As mentioned, an increase in temperature leads to an increase in entropy. This is because as the temperature of a system increases, the particles within the system gain more energy and move around more, leading to a more disordered state.

3. Can entropy decrease with increasing temperature?

No, according to the Second Law of Thermodynamics, entropy will always increase with an increase in temperature. It is possible for the entropy to remain constant, but it cannot decrease.

4. Is there a mathematical relationship between entropy and temperature?

Yes, the mathematical relationship between entropy and temperature is expressed as dS = dQ/T, where dS represents the change in entropy, dQ represents the transfer of heat, and T represents the temperature of the system.

5. How does the concept of entropy relate to everyday life?

Entropy is a fundamental concept in understanding the behavior of thermodynamic systems, but it also has applications in everyday life. For example, entropy can explain why an ice cube melts in a warm room or why a hot cup of coffee cools down over time. It can also be used to understand the spontaneous processes that occur in nature, such as water flowing from a high point to a low point.

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