Energy Flashcards
What is flow energy?
Energy required to push an element across a boundary FE = pressure*volume
What is heat flux?
heat transferred per unit time per unit area available for heat transfer (q). This has units of W/m^2
Specific heat capacity at constant volume, Cv
used in cases where the volume is constant and the pressure varies Change in internal energy = m*Cv*(T1-T2)
Specific heat at constant pressure, Cp
This is the specific heat, which should be used in flow situations where volumes are changing but pressure is constant. Enthalpy change = m*Cp*(T1-T2)
How are Cp and Cv related?
Cp=Cv+R R is the gas constant ( 8.31 J/K mol)
What is latent heat?
Energy required to change the phase of a substance from one phase to another.
Determine the heat required to thaw 100 kg of frozen orange juice, bring it to the boil and evaporate 25 kg of water from the juice. The process takes place at atmospheric pressure. Use: Initial juice temperature = -10C Freezing point of juice = 0C Boiling point of juice = 100C Specific heats: frozen juice = 2.01 kJ/kgK; liquid juice = 3.98 kJ/kg K Latent heats: fusion = 333.2 kJ/kg; vaporisation = 2257 kJ/kg
heat the frozen juice from -10 to 0C: requires 𝑚 𝐶𝑝𝑖𝑐𝑒∆𝑇 (ii) melt the juice: requires 𝑚∆ℎ𝑓𝑢𝑠𝑖𝑜𝑛 (iii) heat the liquid juice from 0 to 100C: requires 𝑚 𝐶𝑝𝑙𝑖𝑞∆𝑇 (iv) boil the juice: requires 𝑚∆ℎ𝑒𝑣𝑎𝑝 So the heat needed is (i) 100*2.01*10+100*333.2+100*3.98*100+25*2257 = 131 555 kJ
What is Fourier’s law?
Q=k*A*ΔT /x
Q is rate of transfer (W) k is thermal conductivity of a material (W/mK) A is area ΔT is temperature difference x is thickness
What is the equivalent of thermal resistance?
R= X/(K*A)
How are thermal resistances added in parallel ?
The same way there are added in electricity
For a cylinder with multiple layers, how is thermal resistance found for a general layer?
= (1/2πL)*ln((Rn+1)/Rn)* (1/K) Rn is the inner layer
How is Q found with thermal resistance?
Q=ΔT/R
How is the rate of heat transfer found from pipe with many layers?
Find the thermal resistance for each layer. Sum together and use Q=T/R
What is convection?
Energy transfer from an area of high temperature to low temperature by mixing.
Natural convection?
Mixing induced by density differences due to temperature gradients.
Forced convention?
Mixing caused by an external force e.g. pump/fan
What is h? How is it found?
Local heat transfer coefficient (W/km^2) K/ width of convection layer
How do you find Q across a convection layer?
Q=h*area*ΔT
Nu
(h*d)/k k is thermal conductivity of fluid
Pr
(SHC of fluid) * (viscosity) / k
Gr
L3ρ2β*g*ΔT / viscosity2
β =(mean tempeture of surface)-1
Re
(L*u*ρ)/μ
With a convection current along a surface, where does laminar flow end?
A distance that gives Re = 5*105
For laminar flow, what formula gives the speed distrbution in a pipe?
u=U*(1-(r2/R2))
Where U is the speed at the centre, R is the radius and r is the radius measured from the centre.
How is the average speed found for laminar flow in a pipe?
U/2
What formula gives the velocity distrbution in a pipe with turbulant flow?
u=U*(1-(r/R))^(1/7)
R is the pipe radius and r is the distance measured from the centre of the pipe
How is the mean speed found in a pipe showing turbulant flow?
mean=0.8*U
What are the properties of a black body?
Absorbs all incident radiation.
For a given temperture and wavelength no body can emit more than a black body.
The radiation emitted by blackbody is a function of wavelength and temperature but it is independent on direction and its construction, e.g. blackbody is a diffusive emitter.
spectral emissive power
the rate at which radiation at wavelength λ is emitted in all directions per unit surface area.
As temperture increases, it produces lower wavelengths.
Wien’s displacement law
It states that the product of the wavelengths at maximum spectral emission power and temperature is constant:
λmax *T =C3 ,
where C3 =2897.8 ( μm*K) is the third radiation constant
Stefan-Boltazman law.
The total emissive power of black body (radiation emitted in all directions) over entire wavelengths is proportional to 4th power of absolute temperature of blackbody.
Eb=δ*T4
δ is the stefan-boltzman constant.=5.67*10-8 (W m-2 K-4)
What is absorpivity?
Also known as emissivity (ε)
Equal to energy absorbed/total energy
1 for black bodies.
What does q denote?
Q/area
What is the equation to find the heat transfer by radiation between grey bodies?
What is the sign convention with heat transfer
Q into system from surroundings and work on system +
Q out of the system to surroundings and work done by system (expansion) -
Intensive properties
If you had a system and only looked at half of it, they would be the same
e.g. temperture, pressure, density, specific heat, specific entropy
Extensive properties
Mass, volume, total energy, work done, enthalpy
What is u?
Specific internal energy (opposed to internla engergy U)
What is specific volume?
Volume / mass
How do you find work done at constant pressure?
Pressure *change in volume
What is the equation for an adiabatic process?
p*vν=constant
(ratio of specific heats )ν=Cp/Cv 1.4 for air
What does adiabatic mean?
No heat in or out
Q=0
What does isentropic mean?
Adiabatic and reversible
What does polytropic mean?
Heat comes in and out
What is the equation for a polytropic process?
pvk=constant
p and v are specific values.
k is the process index (found through experimentaion)
On a PV diagram, which curve will be at a higher temperture?
The one further away from the origin
What is an isothermal process?
One at constant temperture
(Thus change in internal energy =0)
How can you find work for an isothermal process?
work=C*ln(V1/V2)
c=P1V1
How do you find the work in a polytropic process?
Work =(1/k-1)*(P2V2-P1V1)
What is a closed system?
One with no mass transfer.
What is a uniform system?
Constant in space
Steady state?
Constant in time. No collection or loss of mass.
How do you find the enthalpy of a system?
H=U+PV
What is the equation for specific enthalpy?
h=u+pv
u is specific internal energy and v is specific volume
h=H/m
Where H is enthalpy and m is the mass
How do you find total internal energy?
U=m*Cv*T
What is a bar?
100,000 Pa
In the pV=mRT, what is R?
The universal gas constant, 8.31 J/mol K
What is the specific gas constant?
The gas constant / molar mass of gas.
Cp-Cv
In the stegan-boltzman law, wha is E
Watts/ metre2
What is k on the equation sheet?
Thermal conductivity
What are the units in the ideal gas equation?
K
How do you find the work in an iscentropic process?
(P2V2-P1V1) / (υ-1)
