The First Law of Thermodynamics

The First Law of Thermodynamics Open System (Control Volume)

First low of thermodynamics for open Systems • Reminder of an open System. • Open system = Control volume • It is a properly selected region in space. • Mass and energy can cross its boundary.

Control volume involves two main processes • Steady flow processes. • Fluid flows through the control volume steadily. • Its properties are experiencing no change with time at a fixed position. • Unsteady flow processes. • Fluid properties are changing with time.

Mass balance for steady flow processes • We already showed that for steady flow • Many engineering devices involve a single stream (one inlet and one exit only).

Energy Balance for Steady-Flow Systems 0

Let us look at some common steady flow devices More than one inlet and exit Only one in and one out

For single stream steady flow devices, the 1st low becomes Often the change in kinetic energy and potential energy is small. Per unit mass

Nozzles A1 A2 A nozzle is a device that increases the velocity of a fluid at the expense of pressure

A1 A2 Diffusers A diffuser is a device that slows down the velocity of a fluid causing an increase in its pressure

Diffusers

Nozzles and Diffusers (1st low analysis) NO Is there work in this system? let us say: NO Is there heat transfer? In fact, it depends on the problem! Does the fluid change elevation? NO

In a nozzle, enthalpy is converted into kinetic energy How can you find the mass flow rate in a nozzle?

Example (4-9): Deceleration of Air in a Diffuser • Air at 10oC and 80 kpa enters the diffuser of a jet engine steadily with a velocity of 200 m/s. The inlet area of the diffuser is 0.4 m2. The air leaves the diffuser with a velocity that is very small compare to the inlet velocity. • Determine • (1) The mass flow rate of the air and • (2) The temperature of the air leaving the diffuser.

Example (4-10): Acceleration of Steam in a Nozzle Steam at 1.72 Mpa (250 psia) and 371C (700 F) steadily enters a nozzle whose inlet area is 0.019 m2 (0.2 ft2.) The mass flow rate of the steam through the nozzle is 4.54 kg/s (10 lbm/s) . Steam leaves the nozzle at 1.38 Mpa (200 psia) with a velocity of 274.3 m/s (900 ft/s). The heat losses from the nozzle per unit mass of the steam are estimated to be 2.8 KJ/kg (1.2 Btu/lbm). Determine: (a) the inlet velocity and (b) the exit temperature of the steam. Answers: a) 41.0 m/s or 134.4 ft/s, b) 350 C or 661.9 F

Solution of Example: Acceleration of Steam in a Nozzle Note that there is heat transfer (Q).So, you have to go back to the general form of the 1st low for single stream devices and get the following:

Turbines A turbine is a device that produces work at the expense of temperature and pressure. As the fluid passes through the turbine, work is done against the blades, which are attached to a shaft. As a result, the shaft rotates, and the turbine produces work.

Compressors A compressor is a device that increases the pressure of a fluid by adding work to the system. Work is supplied from an external source through a rotating shaft.

Turbines and Compressors Yes! Is there work in this system? Is there heat transfer? Negligible because of insulation. Exception: Internal cooling in some compressors. Does the fluid change elevation? NO Usuallyit can be ignored Does the kinetic energy change?

Example (4-12): Power Generation by a Steam Turbine The power output of an adiabatic steam turbine is 5 MW, and the inlet and the exit conditions of the steam are as indicated in the figure on the right. a) Compare the magnitude of h, ke, and pe. b) Determine the work done per unit mass of the steam flowing through the turbine. c) Calculate the mass flow rate of the steam. Answers: a) h = -885.9 kJ/kg, ke = 14.95 kJ/kg, pe = -0.04 kJ/kg, b) 871.0 kJ/kg, and c) 5.74 kg/s

Throttling Valve A throttling valve reduces the fluid pressure. P1>P2 It is small device and thus the flow through it may be assumed adiabatic (q=0) since there is neither sufficient time nor large enough area for any effective heat transfer to occur.

Throttling Valve NO Is there work in this system? Is there heat transfer? Usuallyit can be ignored NO Does the fluid change elevation? Usuallyit can be ignored Does the fluid change velocity?

What happens to the fluid temperature a cross throttling Valves ?

Throttling Valves (incompressible substance ) For incompressible substance (like water),  is constant and For incompressible substance only!

Throttling Valves (compressible substance: Vapor) Example (4-13): Expansion of Refrigerant-134a in a Refrigerator Refrigerant-134a enters the capillary tube of a refrigerator as saturated liquid at 0.8 MPa and is throttled to a pressure of 0.12 MPa. Determine the quality of the refrigerant at the final state and the temperature drop during this process. <Answers: 0.339, -53.69oC>

Solution of Example: Expansion of Refrigerant-134a in a Refrigerator Notice that T2 <T1

Throttling Valves (Compressible substance: an Ideal Gas) • What happens if the gas is ideal? • For ideal gases • h = Cp  T But  h = 0 • So…  T = 0 • The inlet and outlet temperatures are the same!!!

Mixing Chamber Mixing two or more fluids is a common engineering process The mixing chamber does not have to be a distinct “chamber.” An ordinary T-elbow, or a Y-elbow in a shower, for example, serves as the mixing chamber for the cold- and hot-water streams as shown in the figure (Left).

Mixing Chamber We no longer have only one inlet and one exit stream Is there any work done? No Is there any heat transferred? No Is there a velocity change? No No Is there an elevation change?

Mixing Chamber • Material Balance • Energy balance

Example(4-14): Mixing of Hot and Cold Waters in a Shower Consider an ordinary shower where hot water at 140oF is mixed with cold water at 50oF. If it is desired that a steady stream of warm water at 110oF be supplied, determine the ratio of the mass flow rates of the hot to cold water. Assume the heat losses from the mixing chamber to be negligible and the mixing to take place at a pressure of 20 psia. <Answer: 2.0>

Heat Exchanger A heat exchanger is a device where two moving fluids exchange heat without mixing.

Heat Exchangers Your analysis approach will depend on how you define your system

Heat Exchangers System (a): entire HX • Mass Balance • Divide into two separate streams with equal inlet and outlet flow rates • Energy balance • Two inlets • Two outlets

Heat Exchangers System (b): Single stream • Mass Balance • Considering one single stream with one inlet and one outlet flow rates • Energy balance • One inlet • One outlet • Plus heat transfer

Example: Cooling of Refrigerant-134a by Water Refrigerant-134a is to be cooled by water in a condenser. The refrigerant enters the condenser with a mass flow rate of 6 kg/min at 1 MPa and 70oC and leaves at 35oC. The cooling water enters at 300 kPa and 15oC and leaves at 25oC. Neglecting any pressure drop, determine (a) the mass flow rate of the cooling water required and (b) the heat transfer rate from the refrigerant to water. <Answers: a) 0.486 kg/s, b) 20.35 kJ/s>

The First Law of Thermodynamics