Energy Balances

Question 0

Non-conservative with decay

Answer 0

Accumulation = input - output - decay

Input = output + decay
= output + KCV

Question 1

Non-conservative with generation

Answer 1

Accumulation = input + output + generation

Question 2

KCV

Answer 2

K: first order reaction rate coefficient
-units: sec^-1, hour^-1, day^-1
C: concentration within the control volume
-e.g. Concentration of pollutant within a lake
V: volume within the control volume
-e.g. Lake volume

Question 3

• Steady state non-conservative system: polluted lake
• WWTP effluent, flow rate: 0.5 m^3/s (Qw) with 100 mg/L (Cw) of pollutant
• incoming stream, flow rate of 5 m^3/s (Qs) with 10 mg/L (Cs) of pollutant
• calculate input rate, output rate, decay rate

Answer 3

• input rate: Cm= (QsCs + QwCw)/ Qm
• output rate: QmCm = (Qs + Qw)C
• decay rate: KCV

Question 4

Energy

Answer 4

• capacity for doing work

* units: Btu, Joule, kWhr, cal

Question 5

Power

Answer 5

• rate of doing work

* units: Watt (J/s), Btu/hr

Question 6

Specific heat capacity (C)

Answer 6

Amount of energy needed to raise the temperature of a unit mass of a substance by 1 degree

Question 7

Latent heat of fusion (enthalpy of fusion)

Answer 7

• energy required to go from solid to liquid state (melting)

* 333 kJ is needed to melt 1 kg of ice

Question 8

Latent heat of vaporization (enthalpy of vaporization)

Answer 8

• energy required to go from liquid to gaseous state

* 2257 kJ is needed to convert 1 kg of H2O at 100C to steam

Question 9

Energy released or absorbed in phase changes…

Answer 9

mL

m= mass (kg or lbs)
L= latent heat of fusion or vaporization (kJ/kg, Btu/lb, kcal/kg)

Question 10

When 2 objects are at different temperatures…

Answer 10

Heat will be transferred from the hotter to the colder object

Question 11

Mechanisms of transfer can be…

Answer 11

Conduction: direct physical contact
Convection: liquid or a gas medium
Radiation: can be in the absence of any physical medium

Question 12

Objects emit EM radiation as a function of their temperature and surface area

Answer 12

Higher T -> more EM radiation -> shorter wavelength (λ)

Question 13

Wien’s Displacement Rule

Answer 13

• determines wavelength of maximum radiation

* λ(μm) = 2898/ T (K)

Question 14

Earths average temperature is

Answer 14

15C

Question 15

What is the Sun’s wavelength of maximum radiation?

Answer 15

λ(μm)= 2898/ (15+273.15)= 10.06 μm

Question 16

Greenhouse gases permit ______ wavelengths (from the sun) to pass through but absorb ______ wavelengths radiated by the earth resulting in a ______ effect

Answer 16

1. Shorter
2. Longer
3. Warming