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Alex17521 [72]
3 years ago
9

Two containers (A and B) are in thermal contact with an environment at temperature T = 280 K. The two containers are connected b

y a tube that contains an ideal turbine (a mechanical device) and a valve. Initially, the valve is closed. Container A (volume VA = 2 m3) is filled with n = 1.2 moles of an ideal monatomic gas, and container B (volume VB = 3.5 m3) is empty (vacuum). When the valve is opened, gas flows between A and B, and the turbine is used to generate electricity. What is the maximum amount of work than can be done on the turbine as the gas reaches equilibrium? Remember: U = 1.5 nRT + const S = nR ln(V) + f(U,n)
Physics
1 answer:
zmey [24]3 years ago
8 0

Answer:

The maximum amount of work is  W = 1563.289 \ J

Explanation:

From  the question we are told that

   The temperature of the environment is  T = 280\ K

    The volume of container A is  V_A = 2 m^3

    Initially the number of moles  is  n = 1.2 \ moles

     The volume of container B is V_B = 3.5 \ m^3

     

At equilibrium of the gas the maximum work that can be done on the turbine is mathematically represented as

             W =  P_A V_A  ln[ \frac{V_B}{V_A} ]

Now from the Ideal gas law

          P_A V_A =  nRT

So substituting for P_A V_A in the equation above

          W =  nRT ln [\frac{V_B}{V_A} ]

Where R is the gas constant with a values of  R =  8.314 \  J/mol

Substituting values we have that

            W = 1.2 * (8.314) * (280) * ln [\frac{3.5}{2} ]

          W = 1563.289 \ J

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