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Thermodynamics Questions - Answers and Solutions

## Question 1: The State Postulate, Reversible Processes, and Closed Systems

Answer the following questions using statements, proofs, calculations, or examples. No marks will be given for guesses.

(i) What is the state postulate? (3)

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(ii) Show that heat transfer must be done isothermally for the process to be reversible. (3)

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(iii) True or false: the cyclic integral of work must be zero for any process. (Explain your answer as indicated above) (3)

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(iv) By employing the first and second laws of thermodynamics (and whatever else you require), derive an expression for the reversible work of a closed system. (8)

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(v) A window air conditioner that consumes 1 [kW] of electricity when running and has a coefficient of performance of 3 is placed in the middle of a room and is plugged in. What is the net effect of running the air conditioner in the room? (3)Â

A water pump is used to transfer water from an open basin to a large tank. The pump consumes 4.0 [kW] of electricity operating at steady state and draws in liquid water at 100 [kPa], 15 [Â°C] with a mass flow rate of 4.5 [kg/s]. You may assume that there is no significant difference between the inlet and outlet diameters and the elevation between the inlet and outlet is small. The local acceleration due to gravity is 9.81 [rn/s2]. Starting from the general forms of the laws of thermodynamics given in the Equation Aid, determine the highest pressure that the pump can operate against?Â

A vapor-compression refrigeration system circulates refrigerant 134a at a rate of 6 [kg/min]. The refrigerant enters the compressor at -10 [Â°C], 140 [kPa] and exits at 700 [kPa]. The isentropic efficiency of the compressor is 67%. There are no appreciable pressure drops as the refrigerant flows through the condenser and evaporator. The refrigerant leaves the condenser at 700 [kPa], 24 [Â°C]. Ignoring heat transfer between the compressor and the surroundings, determine:

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(i) the compressor work in [kW],

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(ii) the heat transfers associated with the condenser and evaporator in [kW],

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(iii) the coefficient of performance, C.O.P., of the system,

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(iv) the entropy generation for the condenser process, and

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(v) the theoretical limit for the coefficient of performance.

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A steam turbine is used to generate power at a small-scale power plant. The turbine is well-insulated and operates at steady-state with steam entering at 5 [MPa] and 600 [t]. The steam exits the turbine as a saturated vapour at 50 [kPa]. Kinetic and potential energy effects are negligible. Starting from the general forms of the thermodynamic laws given in the Equation Aid, determine:

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(i) The work developed by the turbine in kJ per kg of steam flowing through the turbine, and

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(ii) The isentropic efficiency of the turbine.Â

Consider the filling of a tire using an air-line that supplies air at a constant condition of 700 kPa and 20 M. The tire is initially at a pressure of 135 [kPa] (5 psig) and is in thermal equilibrium with its surroundings at 20 M. The tire is then filled to the manufacturer recommended 322 [kPa] (32 psig), where its volume is 10 [L]. Prior to filling, it was found that the volume of air in the tire was 8.5 [L]. For simplicity, the fire can be assumed to be a linear elastic material where the pressure varies linearly with respect to its volume. Starting from the general forms of the thermodynamic laws given in the Equation Aid, determine the work done during the filling process and the final temperature of the air in the tire. You may assume that the process is adiabatic, and that nominal values of the specific heats can be used (fable A-2). Based on your result, is the assumption that the process is adiabatic reasonable?Â