# Entropy Change in a Reversible Process multiple phase change

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In summary, the question is asking for the amount of heat needed to convert 0.120kg of frozen ammonia from 100oC to a gas at 80oC, as well as the total entropy change associated with this process. The heat added is 2.36 x 105J, and the integral for the entropy change is computed separately for the different stages of the process, resulting in a total entropy change of 865 J/K.
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## Homework Statement

(a)How much heat must be added to a block of 0.120kg of frozen ammonia initially at 100oC to convert it to a gas at 80oC given the following information?
(b) assuming this could be done using a reversible process what would be the total entropy change associated with this operation given that ΔS=∫dQ/T (from b to a where b= Ti and a=Tf
T melt = -78 C
Tvap = -33 C
c solid = 2030
Lf = 332000
C liquid = 4750
Lv=1370000
c, gas = 28
M = 17.0 g/mol

ΔS=∫dQ/T

## The Attempt at a Solution

I've figured out the first part the heat added is simply 2.36 x 105J

But I can't seem to get the second part analyzing the integral:
$$ΔS= \int_{173.15K}^{353.15K}\frac {dQ} T \$$
where $$dQ = mcdT$$

by integrating the function I get:

$$ΔS =0.120kg * 4750J/kgK *( ln(353.15) - ln(173.15))$$

I get ~ 400 J/K as an answer and the actual answer is 865 J/K ... I don't get what I'm doing wrong, is this the right path to take or am I actually suppose to take the integral from init Temp to melting point temp then from melting point temp to vaporization temp then to 80 oC ?

You must compute the entropy change separately for the different stages:
1. 173K to 195K
2. heat of fusion at 195K
3. 195K to 240K
4. heat of vaporization at 240K
5. 240K to 353K

That's 3 different integrals and two "gimmes" to compute the entire change in S.

## 1. What is entropy change in a reversible process multiple phase change?

Entropy change in a reversible process multiple phase change refers to the change in the amount of disorder or randomness in a system as it undergoes a reversible phase change. It is a measurement of the energy distribution within a system and is closely related to the concept of thermodynamic entropy.

## 2. How is entropy change calculated in a reversible process multiple phase change?

The entropy change in a reversible process multiple phase change can be calculated using the formula ΔS = Q/T, where ΔS is the change in entropy, Q is the heat added or removed from the system, and T is the temperature of the system in Kelvin.

## 3. Why is entropy change important in a reversible process multiple phase change?

Entropy change is important in a reversible process multiple phase change because it is a fundamental concept in thermodynamics that helps us understand the direction and efficiency of energy transfer. It also plays a crucial role in determining the spontaneity of a process.

## 4. How does entropy change in a reversible process multiple phase change affect the behavior of a system?

The change in entropy in a reversible process multiple phase change affects the behavior of a system by determining the amount of energy that is available to do work. An increase in entropy results in a decrease in the amount of available energy, and vice versa.

## 5. Can entropy change be reversed in a reversible process multiple phase change?

Yes, entropy change can be reversed in a reversible process multiple phase change. This means that the system can return to its initial state without any net change in entropy, as long as the process is carried out in a reversible manner. This is the basis of the concept of reversibility in thermodynamics.

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