First Law Thermodynamics Professor Lee Carkner Lecture 4

PAL # 3 Energy  Energy generation potential of a river  Energy in river = e mech = (P/  )+(v 2 /2)+gz  Pressure is negligible and v = 3 m/s, z = 30 m  e mech =  Need mass flow rate = m’ =  v’ = (1000)(500) = kg/s  E’ = m’e mech =  Actual output power depends on efficiency of turbine

PAL # 3 Energy  Energy generation potential of wind turbine  Only important energy is ke  e mech = (v 2 /2) =  Need mass flow rate = m’ =  V’  V’ = Av = (  D 2 /4)(10) =  m’ = (28274)(1.25) = kg/s  E’ = m’e mech =  Number of turbines to equal dam energy output   Note:   Water is easier to control

First Law of Thermodynamics  Total energy is conserved   Hard to see sometimes because energy transfer by heat is hard to measure  We can write the first law as:   E sys = E in -E out    E sys = m  u+½m(  v) 2 +gm  z

Adiabatic  An adiabatic process has no heat transfer  Adiabatic processes might be:   At same temp as surroundings   All adiabatic processes between the same two states require the same work   an adiabatic process can never be isothermal

Energy Transfer  Energy can be transferred into a system in 3 ways:  Heat:   Changes internal energy  Work:   Can change any system energy  Mass flow:   Energy of the mass can be in different forms

Energy Balance  General expression:   E sys = E in -E out  In rate form:  For constant rates:  E =(dE/dt)  t

Efficiency  Efficiency relates the input and output of a system:   This is the engineering efficiency   Not to be confused with the economic efficiency   Devices with high engineering efficiency are not always the most cost effective to use

Flow Device Efficiency  Mechanical Efficiency  mech = E mech,out /E mech,in = 1 – (E mech,loss /E mech,in )   For a pump that supplies mechanical energy to a fluid:  pump = (energy increase of fluid) / (energy used by pump) = E fluid /E pump   For a turbine that extracts energy from a fluid  turbine = (energy output) / (energy decrease of fluid) = E turbine /E fluid

Electrical-Mechanical Efficiency   Produces rotating mechanical energy  motor = (mech. power output) / (elec. power input)   generator = (elec. power output) / (mech. power input)   The combined efficiency is just the product of the efficiency of each component

Combustion   Efficiency is related to the heating value of the fuel (HV)   Actual efficiency is:   Will be less then 1 if exhaust is hot or not all fuel is consumed

Combustion and Cost  High efficiency gas furnaces and water heaters extract as much heat from the exhaust as possible before venting   Not always cost effective   Gas is cheaper than electricity

Producing Electricity  To produce electricity:   Use heat to expand a fluid and turn a turbine   Total efficiency is:  powerplant =  Electricity is very convenient, but the grand total efficiency of electrical appliances is low

Lighting Efficiency   100 W lightbulbs all have 100 W as input, but different outputs   Sodium vapor lamps can be 10 times more efficient than incandescent but produce yellow light 

Next Time  Read:  Homework: Ch 2, P: 114, Ch 3, P: 22, 36, 47