Which of the following statements is true for an adiabatic turbine that operates at steady state but is not reversible? Assume “the system” is defined as the fluid inside the turbine.
A. The generation term in the entropy balance is zero, but the change in entropy of the universe is positive.
B. The change in entropy of the universe is positive, but the change in entropy of the system could be positive, negative or zero.
C. The specific entropy of the fluid leaving the turbine has to be equal to the specific entropy of the fluid entering the turbine, because the turbine is at steady state.
D. The efficiency of the turbine can be greater than 1, but only if the entering steam is superheated rather than saturated.
E. None of the above is true.
A. Incorrect. A non-reversible process generates entropy by definition.
B. Incorrect. In order for the system to be at steady state, the change in entropy of the system has to be zero. Entropy is generated, but the entropy of the exiting stream is larger than the entropy of the entering stream, so there is no accumulation of entropy.
C. Incorrect. This would be true if the system were, like in Example 4-6, an adiabatic, reversible and steady-state process. But in an irreversible process, the generation of entropy leads to the exiting stream having a larger entropy than the entering stream.
D. Incorrect. An efficiency greater than 1 or 100% means the entropy of the universe is being decreased; it violates the second law of thermodynamics (though it doesn’t necessarily violate the first law).
E. Correct. All statements contain at least one conceptual mistake.
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A computer sends a packet of information along a channel and waits for a return signal acknowledging that the packet has been received. If no acknowledgment is received within a certain time, the packet is re-sent. Let X represent the number of times the packet is sent. Assume that the probability mass function of X is given by
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d. Find the variance of the number of times the packet is sent.
e. Find the standard deviation of the number of times the packet is sent.