A liquid has a constant CP=100 J/mol•K. 1 mole of this liquid is confined in a piston-cylinder device, with an initial temperature of T=500 K and pressure P=1 bar. The insulation is removed from the cylinder, allowing it to exchange heat with the surroundings, which can be modeled as a heat reservoir at T=300 K and P=1 bar. The process continues until the liquid in the cylinder reaches equilibrium with the surroundings.
A) Find the change in entropy of the liquid resulting from this process.
B) Find the change in entropy of the universe resulting from this process.
When equilibrium is reached, the final temperature of the liquid will be 300 K for thermal equilibrium with the heat reservoir.
Apply the definition of change in entropy for the liquid. The heat transfer is not reversible, but we use a reversible path to calculate the state property dS:
Where dQ is found through the energy balance of the process:
Where dWEC is negligible in this case assuming the liquid is incompressible (dW_EC= -PdV)
Note: The reversible and irreversible paths will have the same Q, because it is equal to the change in U which is a state property. If there was a significant expansion/contraction work term in the energy balance, the reversible and irreversible Q values wouldn’t be the same.
After substitution:
Substitute dQ into definition of entropy:
After integration where n and CV are treated as constants:
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