3. En Flashcards
Most efficient transformation from heat to exergy in a thermodynamic cycle.
Name the cycle!
Carnot Cycle
Draw the Carnot-Cycle in a pV-diagram and in a Ts-diagram!
Add all important information (e.g. Q,W,…)
p.3
Formula for Carnot efficiency (eta c)?
eta c = 1 - T0/T (T in Kelvin)
Describe the steps of a ideal gas in the Carnot Cycle! (allocate them in the diagram!)
(1->2, 2->3, 3->4, 4->1)
1->2: adiabatic and isentropic compression (so: no heat and no entropy is added; fully reversible as no entropy is added)
2->3: isothermal heat supply (adding heat without changing temp.; can only be done if the fluid has a lot of room to expand)
rest reverse:
3->4: adiabatic and isentropic expansion
4->1 isothermal cooling process
Carnot Cycle
Name the formula for calculating effective work!
Effective work:
-W = Q - IQ0I
((see p.3))
Draw the Joule Process of a Gas Turbine Plant in a pV-diagram and in a Ts-diagram!
Add all important information (e.g. Q,W,…)
p. 4
Joule Process of a Gas Turbine Plant
Name the formula for calculating the effective work!
-W = Win - IWoutI = Qin - IQoutI
Carnot cycle
Name the formula to calculate the thermal efficiency (eta th) (with given effective work -W and Q)!
eta th
= -W / Q
= (Q-IQ0I) / Q
= 1 - IQ0/QI
Ideal gas law and polytropic relations (View from “inside”):
Changes of the internal energy and enthalpy of an ideal gas proportional to the ??.
temperature change
Ideal gas law and polytropic relations (View from “inside”):
Changes of the internal energy and enthalpy of an ideal gas proportional to the temperature change.
1) dh = ??
2) du = ??
3) h = ??
1) dh = cp * dT
2) du = cv * dT
3) h = u + pv
What does cp and cv describe?
Describe how much heat must be supplied to a substance to obtain a temperature change of 1°K
Energy balances (Merging with view from “outside”)
Formula effective power output (P_out)!
P_out
= I Pexp,real I - I Pcom,real I
= Q_punkt_in - Q_punkt_out
Carnot cycle
Name the formula to calculate the thermal efficiency (eta_th):
1) If effective power output (P_out) and Q_ounkt_in are given!
2) If q_out and q_in are given!
3) If T1, T2,T3 und T4 are given!
1) eta_th = IP_outI / Q_punkt_in
2) eta_th = 1 - Iq_outI / q_in
3) 1 - (T4-T1) / (T3-T2)
Thermal efficiency (eta_th):
eta_th
= P_out / Q_punkt_in
= 1 - Iq_outI / q_in
= 1 - (T4-T1) / (T3-T2)
If isentropic
(so if polytropic coefficient(n)=kappa(k)):
(T2/T1)
= (p2/pi)^((k-1)/k)
= (p3/p4)^((k-1)/k)
= (T3/T4)
We get: eta_th = ??
eta_th
= 1 - T4/T3
= 1 - (p1/p2)^((k-1)/k)
= 1 - (p4/p3)^((k-1)/k)
For the efficiency of the joule process only what is relevant?
the pressure ratio
Ideal gas law and polytropic relations (View from “inside”):
The ideal gas equation establishes a relationship between? (3)
pressure, temperature and volume
Ideal gas law and polytropic relations (View from “inside”):
Formula ideal gas equation? (in different forms)
pV = nR_mT
(bzw.: pV = mR_ST)
pv_m = R_mT
(bzw.: pv = R_ST)
With:
R_S: specific gas constant of a gas or a mixture of gases
R_m: general gas constant (bzw. molar gas constant, ideal gas constant or universal gas constant) [8,314 J/(mol*K)]
Formula for calculating the specific gas constant of a gas or a mixture of gases (R_S)?
R_S
= R_m / M
= cp - cv
With:
R_m: general gas constant (bzw. molar gas constant, ideal gas constant or universal gas constant) [8,314 J/(mol*K)]
M: molar mass
cp: specific heat capacity at constant pressure
cv: specific heat capacity at constant volume
Changes of state of ideal gases (from 1-> 2):
I. ?
II. ?
-> Cases (1->2): isotherm, isobaric, isochoric, isentropic -> Welchen Wert hat dann n (polytropic coefficient)?
I.:
(p1 * v1) / T1
= (p2*v2) / T2
II.:
(p2/p1)
= (T2/T1)^(n/(n-1))
= (v1/v2)^n
Cases:
isotherm: T1 = T2, n=1
isobaric: p1 = p2, n=0
isochoric: v1 = v2, n=unendlich
isentropic: P*v^k = const., n = k = cp / cv
With:
cp: specific heat capacity at constant pressure
cv: specific heat capacity at constant volume
k: kappa
kappa air (k_air) hat welchen Wert?
1,4
Energy balances (Merging with view from “outside”)
Assumptions: Heat supply from outside, working fluid is air
1) q12 + wt12
= ??
2) Isobaric heat supply: q12 = ??
3) Isobaric heat removal: qout = ??
4) Isentropic compression: wt,comp,isen = ??
5) Isentropic expansion:
wt,exp,isen = ??
1) (h2-h1) + (c2^2 - c1^2) / 2 + g * (z2 - z1)
2) q12 = h3 - h2
führt zu:
Q_punkt_in = m_punkt_air * cp * (T3 - T2)
3) qout = h1 - h4
führt zu:
Q_punkt_out = m_punkt_air * cp * (T1 - T4)
4) wt,comp,isen
= h2,isen - h1
führt zu:
Pcomp,isen
= m_punkt_air * cp * (T2,isen - T1)
5) wt,exp,isen
= h4,isen - h1
führt zu
Pexp,isen
= m_punkt_air * cp * (T4,isen - T3)
Name to formula to calculate Pcomp,real (isentropic compression real) und Pexp,real (isentropic expansion real)!
Pcomp,real= Pcomp,isen / eta_comp,isen
Pexp,real = Pexp,isen * eta_exp,isen
Geothermal Energy sources
In what groups can geothermal energy sources be divided? (2)
Near-surface geothermal energy
Deep geothermal enegry
Geothermal Energy sources
Near surface geothermal energy: ??
Heat probes and collectors (ca. 5 - 15°C)
Heat and cold storage
(see p.8)
