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------------------------------------------------ A rigid vessel with a volume of 500 liters is divided into two regions with equal volumes. The two regions contain hydrogen, one with a temperature of 350ºC and pressure of 1 MPa, and the other with a pressure of 4 MPa and a temperature of 150ºC.

When the partition breaks, the hydrogen reaches equilibrium, and the temperature becomes 100ºC. Assuming the temperature of the surrounding medium is 25ºC, determine the irreversibility of the process (in kW).

The irreversibility in the process can be calculated as the difference between the actual entropy change and the reversible entropy change at the final equilibrium temperature: Irreversibility = ΔS_actual - R * ln(V_f/V_i) - cp * ln(T_f/T_i)

To determine the irreversibility in the process, we can use the concept of entropy change. The irreversibility in a process can be calculated as the difference between the actual entropy change and the reversible entropy change.

The reversible entropy change can be calculated using the ideal gas equation:

ΔS_rev = R * ln(V_f/V_i) + cp * ln(T_f/T_i)

where:

ΔS_rev is the reversible entropy change

R is the specific gas constant (8.314 J/mol·K)

V_f and V_i are the final and initial volumes, respectively

T_f and T_i are the final and initial temperatures, respectively

cp is the specific heat capacity at constant pressure

Given:

Volume of each region = 500 liters = 0.5 m^3

Initial pressure in region 1 = 1 MPa = 1,000,000 Pa

Initial temperature in region 1 = 350ºC = 623 K

Initial pressure in region 2 = 4 MPa = 4,000,000 Pa

Initial temperature in region 2 = 150ºC = 423 K

Final temperature in equilibrium = 100ºC = 373 K

Temperature of the medium = 25ºC = 298 K

First, let's calculate the reversible entropy change for each region using the given equations:

ΔS_rev_1 = R * ln(V_f/V_i) + cp * ln(T_f/T_i)

ΔS_rev_2 = R * ln(V_f/V_i) + cp * ln(T_f/T_i)

Substituting the given values and using the specific heat capacity of hydrogen (cp = 14.307 J/mol·K), we can calculate ΔS_rev_1 and ΔS_rev_2.

Next, we need to calculate the actual entropy change for the process, which is the sum of the reversible entropy changes of both regions:

ΔS_actual = ΔS_rev_1 + ΔS_rev_2

Finally, the irreversibility in the process can be calculated as the difference between the actual entropy change and the reversible entropy change at the final equilibrium temperature:

Irreversibility = ΔS_actual - R * ln(V_f/V_i) - cp * ln(T_f/T_i)

Substituting the calculated values, we can determine the irreversibility in kW.

Learn more about entropy change from the given link!

https://brainly.com/question/17241209

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