# Finding Isentropic Enthelpy, knowing Isentropic Entropy

• WhiteWolf98
In summary, my question focuses solely on the part of the refrigeration cycle to do with the compressor, where the cycle begins. The first state is before the refrigerant enters the compressor, and the second state is after the refrigerant leaves the compressor. My goal is to obtain 246.37 kJ/kg; but for that, I need 0.9724 kJ/kg.
WhiteWolf98
Homework Statement
The source question is very long, and most likely unneeded. This question is about an actual refrigeration cycle. For the first part of the question, I'm to use the given isentropic efficiency to calculate ##h_{2s}##.
##P_1=140~kPa##
##T_1=-10°C##
##P_2=1~MPa##
##\eta = 0.78##
Relevant Equations
##\eta=\frac {h_{2s}-h_1} {h_2 - h_1}##
A short background: My question focuses solely on the part of the refrigeration cycle to do with the compressor, where the cycle begins. The first state is before the refrigerant enters the compressor, and the second state is after the refrigerant leaves the compressor. My goal is to obtain ##h_2##; but for that, I need ##h_{2s}##.

From the Thermodynamic Tables:

##h_1=h(140~kPa,~-10°C)=246.37~kJ/kg##

Easy enough to obtain. All that's left is ##h_{2s}##. From the T-s diagram of the refrigeration cycle, it can be seen that:

##s_{2s}=s_1##

##s_1=s(140~kPa,~-10°C)=0.9724~kJ/kg\cdot K##

So I know that the entropy at state ##2s## is ##0.9724~kJ/kg\cdot K##

Now this is where I'm stuck. I don't know how to get ##h_{2s}##.

State 1 I know for sure the refrigerant is superheated. And state 2, I'm near to certain it's still superheated.

In other questions, I've been able to work out ##h_{2s}## when state 2 is a mixture. I use the entropies to work out quality,

##x=\frac {s-s_f} {s_{fg}}##

And then knowing the quality, work out ##h_{2s}##:

##h_{2s}=x(h_{fg})+h_f##

I can't do that though if they're both superheated. There's no, 'quality' or, 'x', nor any saturated liquid values. This has come up once before this time, and I was unable to answer it then too. Any help would be appreciated.

If it is superheated it's easier. You just need a table for the superheated vapour properties or a graph and you read ##h_2## knowing both ##P_2## and ##s_2s##. A priori I'm not sure how you can deduce if you have a mixture or a superheated gas. But if you have a superheated gas and you try to work out the quality ##x## you should get an absurd result (bigger than 1 for example...) so that might be a way to check things out if you lack experimental data. But pressure is usually plotted in thermodynamics diagrams for water (or other coolants) so if you locate the right point after the compression took place you should be able to see wether you have a mixture or not. Hope this helps.

WhiteWolf98
Let me guess. Your refrigerant is 134a. Look in your superheated vapor tables at 10 bars and about 55 C.

WhiteWolf98
Greetings to you both. I arrived at my solution, acting on your advice. It was achieved through interpolation.

Using interpolation, I found the temperature to be around ##56.1°C##. Using interpolation again, and that value for temperature, I found the enthalpy (##h_{2s}##) at that temperature to be around ##289~kJ/kg##. I only had table values for ##50## and ##60## degrees, which is why I had to interpolate.

Thanks for the help! You have my gratitude.

WWGD, dRic2 and Chestermiller

## What is Isentropic Enthalpy?

Isentropic Enthalpy is a thermodynamic property that represents the energy content of a system at constant entropy. It is typically denoted as h and is measured in units of energy per mass, such as joules per kilogram.

## What is Isentropic Entropy?

Isentropic Entropy is a thermodynamic property that measures the amount of disorder or randomness in a system. It is typically denoted as s and is measured in units of energy per temperature, such as joules per kelvin.

## How do I calculate Isentropic Enthalpy?

Isentropic Enthalpy can be calculated using the equation h = u + Pv, where u is the internal energy, P is the pressure, and v is the specific volume. Alternatively, it can also be calculated by using tables or charts provided in thermodynamic textbooks or software.

## How is Isentropic Enthalpy used in thermodynamics?

Isentropic Enthalpy is an important property in thermodynamics as it allows for the analysis of energy transfers and transformations in a system. It is often used to calculate the work and heat involved in a process, and it is also used in the design and analysis of thermodynamic systems.

## What is the relationship between Isentropic Enthalpy and Isentropic Entropy?

Isentropic Enthalpy and Isentropic Entropy are related through the concept of entropy. In an isentropic process, the entropy of a system remains constant, and therefore, the change in Isentropic Enthalpy is equal to the change in Isentropic Entropy multiplied by the system's temperature. This relationship is described by the equation dh = Tds.

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