Interpretation:
The change in entropy should be determined for CO2 and N2 blending together to form a gas mixture at same conditions assuming them to be ideal gases.
Concept introduction:
The internal energy change for any reversible process is written as:
Where, dU is change in internal energy, dS is change in entropy and dV is change in volume.
Here, T is temperature and P is pressure.
Ideal gas equation is given by:
PV = nRT
Where, P = Pressure
V = volume
n = number of moles
R = gas constant
T = temperature
And, total entropy change is identified by adding the change in entropy for individual gases.
That is, ΔStotal =ΔS1 +ΔS2
Explanation of Solution
Given Information:
Initial volumes of the gases are:
Final Volume
Pressure of each gas is
Temperature is
Step1:
Establish equation for entropy change.
Since, after mixing there has been no change in internal energy. So, the dU term will become zero such as:
Hence, change in entropy can be written as:
Further, the gases are considered to be ideal and so as per ideal gas equation:
Putting the value of P/T in change in entropy equation we get:
The equation can be simplified as:
Step2:
Entropy change for
Moles of
Adding the values we get:
Hence,
Step3:
Entropy change for N2 gas is calculated as.
Moles of N2;
Adding the values we get:
Hence,
Step4:
Total entropy change is calculated by adding the change in entropy for individual gases as follows:
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Chapter 10 Solutions
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