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Energy Balances on Open Systems at Steady-State

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Energy Balances on Open Systems at Steady-State

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    1. CHEE 221 Lecture 22 1 Energy Balances on Open Systems at Steady-State Open System material crosses the system boundary as the process occurs (e.g., continuous process at steady-state). In an open system, work must be done to push input fluid streams at a pressure Pin and flow rate into the system, and work is done by the output fluid streams at pressure Pout and flow rate on the surroundings as it leaves the system.

    2. CHEE 221 Lecture 22 2

    3. CHEE 221 Lecture 22 3 Steady-State Open System Energy Balance The general balance equation for an open system (i.e., continuous process) at steady-state is:

    4. CHEE 221 Lecture 22 4 Steady-State Open System Energy Balance If is the total rate of energy transport for j input and output energy streams,

    5. CHEE 221 Lecture 22 5 Steady-State Open System Energy Balance

    6. CHEE 221 Lecture 22 6 Notes on Energy Balances for an Open System Possible Simplifications: if Tsystem = Tsurroundings, then Q = 0 since no heat is being transferred due to temperature difference if the system is perfectly insulated, then Q = 0 (system is adiabatic) since no heat is being transferred between the system and the surroundings if energy is not transferred across the boundary by a moving part (e.g., piston, impeller, rotor), then if inflow and outflow streams are of the same velocity, then if there is no large vertical distance between the inlets and outlets of a system, then if system is at constant temperature (system is isothermal), no phase changes or chemical reactions are taking place, and only minimal pressure changes, then

    7. CHEE 221 Lecture 22 7 Problem 7.18 F&R Define a system and simplify the open-system energy balance for each of the following cases. State when possible whether nonzero heat and shaft work terms are positive or negative. Steam enters a rotary turbine and turns a shaft connected to a generator. The inlet and outlet steam ports are at the same height. Some energy is transferred to the surroundings as heat. A liquid stream flows through a heat exchanger in which it is heated from 25?C to 80?C. The inlet and outlet pipes have the same diameter, and there is no change in elevation between these points. A chemical reaction takes place in a continuous reactor that contains no moving parts. Kinetic and potential energy changes from the inlet to outlet are negligible.

    8. CHEE 221 Lecture 22 8 Problem 7.18 F&R Contd (d) Water passes through the sluice gate of dam and falls on a turbine rotor, which turns a shaft connected to a generator. The fluid velocity on both sides of the dam is negligible, and the water undergoes insignificant pressure and temperature changes between the inlet and outlet. (e) Crude oil is pumped through a cross-country pipeline. The pipe inlet is 200 m higher than the outlet, the pipe diameter is constant, and the pump is located near the midpoint of the pipeline. Energy dissipated by friction in the line is transferred as heat through the wall.

    9. CHEE 221 Lecture 22 9 Example Five hundred kilograms per hour of steam drives a turbine. The steam enters the turbine at 44 atm and 450?C at a linear velocity of 60 m/s and leaves at a point 5 m below the turbine inlet at atmospheric pressure and a velocity of 360 m/s. The turbine delivers shaft work at a rate of 70 kW, and the heat loss from the turbine is estimated to be 104 kcal/h. Calculate the specific enthalpy change associated with the process.

    10. CHEE 221 Lecture 22 10 Summary on Energy Balances The First Law of Thermodynamics for a closed (i.e. batch) system is: and the First Law of Thermodynamics for an open system at steady-state (i.e., continuous) system is:

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