S. Yao MECH3310 Lecture 2 Ch 1.3-1.4 05/02/2016 1

Conservation of Energy

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Review of ThermodynamicsEnergy can have many forms

Energy can change from one form to another

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Review of Thermodynamics Energy can exist in numerous forms such as:

mechanical (kinetic, potential), electrical, magnetic, thermal, chemical, nuclear.

Their sum constitutes the total energy E of a system.

The sum of all microscopic forms of energy is called the internal energy u of a system, which consists of - Usensible: translational, rotational, vibration motion of atoms/molecules.- Ulatent: intermolecular forces influencing phase change b/w solid, liquid, vapor.- Uchemical: energy stored in chemical bonds b/w atoms.- Unuclear: binding forces in the nucleus

In heat transfer system, we focus on Usens and Ulat, which are together referred as thermal energy, Ut . The stored mechanical and thermal energy is:

Est = KE + PE + Ut,, where Ut = Usens +Ulatwhile other forms of energy are regarded as Egen (e.g., electrical, nuclear, or chemical, etc).

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Internal Energy u, and Enthalpy h In the analysis of systems that

involve fluid flow, we frequently encounter the combination of internal energy u and pv.

The combination is defined as enthalpy (h =u + pv).

The term pv represents the flow energy of the fluid (also called the flow work).

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Specific Heats of Gases, Liquids, and Solids

Specific heat is mathematically defined as the amount of heat required to raise the temperature of a unit mass of a substance by one unit of temperature

Two kinds of specific heats: specific heat at constant volume cv,

specific heat at constant pressure cp.

The specific heats of a substance, in general, depend on two independent properties such as temperature and pressure.

For an ideal gas, however, they depend on temperature only.

dTmcdU V

dTmcdH p

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Specific Heats of Gases, Liquids, and Solids

At low pressures all real gases approach ideal gas behavior, and therefore their specific heats depend on temperature only.

A substance whose specific volume (or density) does not change with temperature or pressure is called an incompressible substance.

The constant-volume and constant-pressure specific heats are identical for incompressible substances. cv = cp = c

The specific heats of incompressible substances depend on temperature only.

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The First Law of Thermodynamics

The first law of thermodynamics states that energy can neither be created nor destroyed during a process; it can only change forms.

The energy balance for any system undergoing any process can be expressed as (in the rate form)

Total energyentering the

system

Total energyleaving the

system

Change in thetotal energy of

the system- =

Rate of net energy transferby heat, work, and mass

Rate of change in internal kinetic, potential, etc., energies

(W)in out systemE E dE dt

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At an Instant of Time:

Note representation of system by a control surface (dashed line) at the boundaries.

Energy Conservation for a Control Volume

,

Surface Phenomena

Rate of thermal and/or mechanical energy transfer across the control surface due to heat transfer, fluid flow and/or work interactionoutin

EE ,

Volumetric Phenomena

Rate of thermal energy generation due to conversion from another energy form (e.g., electrical, nuclear, or chemical); energy conversion process occurs with the system

stEgE

Rate of change of energy storage (thermal and/or mechanical) in the system

Conservation of Energy

goutinst EEEE Over a time interval

goutinst EEEE

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Closed systems Stationary closed system, no

work

Steady-Flow Systems For system with one inlet and one

exit:

When kinetic and potential energies are negligible, and there is no work interaction

tst UEWQ

(J)vQ mc T

0W (kg/s)in outm m m

)( inoutp TTcmq

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A special case for no mass or volume passing the control surface,

Holds for steady-state and transient conditions.

Consider surface of wall with heat transfer by conduction, convection and radiation.

With no mass and volume, energy storage and generation (volumetric) are not pertinent to the energy balance, even if they occur in the medium bounded by the surface.

Surface Energy Balance

Conservation Energy (Instant in Time):0 outin EE

0 gst EE

0 radconvcond qqq

0)()( 4422221 surTTTThLTTk

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Example 1.4: (energy balance) Application to thermal response of a conductor with Ohmic heating (generation). Derive the variation of temperature with time during passage of current I.

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Example 1.6: (latent heat) Application to isothermal solid-liquid phase change in a container. If the outer surface of the wall is heated to T1 > Tf to melt the ice, find the time needed to melt the entire mass of ice (M).

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Example 1.9: (surface energy balance) Coating with prescribed radiation properties (, ) is cured by irradiation from an infrared lamp. Heat transfer from coating is by convection to ambient air and radiation exchange with the surroundings. Find the cure temperature for different h.