# Entropy Calculation in Thermodynamics Homework

• ruiwp13
In summary: Homework Statement The equation you used in part (b) is for an ideal gas, but not a liquid. The question must be referring to liquid water, because water can't exist as a vapor at these pressures and 15C. The change in entropy is the amount of energy that is released when the water changes from a liquid to a vapor.
ruiwp13

## Homework Statement

Calculate the variation of entropy in the following processes:
a) Heating of 18 kg of water from 15 to 40ºC at ambient pressure.
b) Compression of 9 kg of water from ambient pressure to 7atm at the temperature of 15ºC.

## Homework Equations

ΔS=Cp*ln(T_final/T_initial)

## The Attempt at a Solution

So for a) I checked the Cp of water getting 4.18KJ/kgºK and multiplied it by the 18 kg. Then I tried to apply the formula with the Cp and the Tfinal=313.15K and TInitial=288.15K and I think it is correct.

For b) I think I have to use ΔS=R ln (P1 / P2) but I'm not sure. And if it is that expression, the Pressure must be in kPa?

Last edited:
ruiwp13 said:

## Homework Statement

Calculate the variation of entropy in the following processes:
a) Heating of 18 kg of water from 15 to 40ºC at ambient pressure.
b) Compression of 9 kg of water from ambient pressure to 7atm at the temperature of 15ºC.

## Homework Equations

ΔS=Cp*ln(T_final/T_initial)

## The Attempt at a Solution

So for a) I checked the Cp of water getting 4.18KJ/kgºK and multiplied it by the 18 kg. Then I tried to apply the formula with the Cp and the Tfinal=313.15K and TInitial=288.15K and I think it is correct.

For b) I think I have to use ΔS=R ln (P1 / P2) but I'm not sure. And if it is that expression, the Pressure must be in kPa?

In part (a) the equation you used applies to liquid water or to an ideal gas at constant volume. I assume you knew you were doing it for liquid water. The equation you used in part (b) is for an ideal gas, but not a liquid. The question must be referring to liquid water, because water can't exist as a vapor at these pressures and 15C. If the temperature doesn't change, what is the change in the internal energy of the liquid water? How much work is done on the water to compress it from 1 atm to 7 atm? How much heat is involved? What is the change in entropy?

Chet

1 person

## 1. What is entropy in thermodynamics?

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it is often referred to as the measure of the amount of unavailable energy in a closed system.

## 2. How is entropy calculated in thermodynamics?

The change in entropy of a system can be calculated by using the equation ΔS = Qrev/T, where ΔS is the change in entropy, Qrev is the reversible heat transfer, and T is the temperature in Kelvin.

## 3. What is the relationship between entropy and temperature?

The relationship between entropy and temperature is that as the temperature of a system increases, its entropy also increases. This is because at higher temperatures, there is more energy available for particles to move and cause disorder in the system.

## 4. How does entropy 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. This means that in any natural process, the total disorder or randomness in a system will always increase.

## 5. Can entropy ever decrease?

While the total entropy of a closed system will always increase, it is possible for the entropy of a specific part of the system to decrease. However, this decrease in entropy must be accompanied by an increase in entropy elsewhere in the system, resulting in a net increase in total entropy.

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