Lecture 7 - Carnot Cycle Flashcards
Heat, Q, and work, W, are path dependent.
True
State functions are path dependent; therefore, heat and work are state functions.
FALSE! Heat and work are path dependent and are therefore not state functions.
State functions are path INDEPENDENT
Internal energy is a state function and is therefore …
independent of the path taken
For an isothermal process, the work done by the system is …
the area under the curve, which can only be solved by calculus and is
W = nRT*ln(V2/V1)
The internal energy of a gas, U, is proportional to …
the temperature
If the temperature does not change, the internal energy …
remains the same
Efficiency, η, is equal to …
η = (work in + heat in)/work out
What is a reversible process?
a process that can be reversed without leaving any trace on the surroundings
a process where the net heat and work exchange between the system and surroundings is 0.
In thermodynamics, we look at work with reversible processes and consider them as ideal because …
they are easier to work work
All real processes (processes in reality) are irreversible processes because …
mechanical friction (pressure drop, surfaces rubbing together)
All real processes (processes in reality) are irreversible processes because …
- mechanical friction (pressure drop, surfaces rubbing together)
- non - quasi equilibrium expansion and compression processes
- heat transfer across “large”/finite differential temperatures
Thermal energy is easy to recover
false
thermal energy is difficult to recover, which is why processes that release thermal energy are irreversible
quasi equilibrium expansion processes are those that …
go very very slowly in order to maintain equilibrium
non - quasi equilibrium expansion and compression processes are those that …
move very quickly and are therefore not in equilibrium
quasi equilibrium expansion and compression processes are those that …
go very very slowly in order to maintain equilibrium
A reversible process has heat transfer occurring across …
an infinitesimally small differential temperature
All heat cycles studied are revesible
FALSE!
they do not meet the criteria for reversibility (opposite of list for irreversibility)
We study reversible processes because …
they give us a good idea on how real world processes are performing with respect to the idealization
Reversible processes deliver …
the largest amount of work (engines/turbines) and require the least amount of work (pumps/ compressors)
for this reason, they are used as theoretical limits
The devices that give us the largest amount of work are …
engines and turbines
The devices that use the least amount of work are ..
pumps and compressors
What is a carnot heat engine?
An engine that operates on 4 reversible processes
The processes of the carnot heat engine are …
- reversible isothermal expansion from state 1 to state 2 at T (hot/ source)
- reversible adiabatic expansion from state 2 to 3
- reversible isothermal compression from state 3 to 4
- reversible adiabatic compression from state 4 to 1
If a gas expands rapidly …
it gets cold
During reversible isothermal expansion from state 1 to 2 in the Carnot heat engine cycle, we have …
heat addition to prevent the gas from cooling
During reversible adiabatic expansion of the Carnot heat cycle, we have …
no heat transfer while the gas expands, so we drop to a lower temperature
If there is no heat transfer when you are expanding a gas, the gas …
gets cooler
During reversible isothermal compression,
the gas gets hotter as the gas compresses, and that heat is ejected to the surroundings from the cycle so the process can remain at the same temperature
During reversible adiabatic compression,
the gas gets hotter, but the heat is not released, causing the temperature to increase as well, taking us from one isotherm to another, higher isotherm.
Although the Carnot cycle is an idealization, we can write an equation for the efficiency of the cycle, η.
η =
η =
Although the Carnot cycle is an idealization, we can write an equation for the efficiency of the cycle, η.
η =
η = (Qh/Ql)rev = Th/Tl
where Qh= heat going into the cycle
Ql = heat leaving the cycle
Th = the higher temperature (in Kelvin)
Tl = the lower temperature (in Kelvin)
The efficiency of a reversible heat cycle, η is equal to …
η = (Qh/Ql)rev = Th/Tl
where Qh= heat going into the cycle
Ql = heat leaving the cycle
Th = the higher temperature (in Kelvin)
Tl = the lower temperature (in Kelvin)
The Carnot engine is a reversible heat engine.
True
The thermal efficiency of a reversible cycle is ….
η = 1 - Ql/Qh = 1 - Tl/Th
What are the Carnot principles?
- the thermal efficiency of an irreversible heat engine is always less than a reversible heat engine operating between the same two reservoirs as the irreversible engine
ηirrev < ηrev - the thermal efficiency of all reversible engines operating between the same two reservoirs are the same
ηrev(a) = ηrev(b)
Draw the Carnot Heat Cycle on a P-v diagram.
1 ↙ Qh
\ ↘ Th
\ 2
\ \ (slightly curved inwards in the center)
4←(Tl) 3
↓ Ql
P on y and v on x
What are the processes in a Carnot heat pump/refrigerator?
- reversible adiabatic expansion from state 1 to state 2
- reversible isothermal expansion from state 2 to 3
- reversible adiabatic compression from state 3 to 4
- reversible isothermal compression from state 4 to state 1
In compression, the pressure goes ….
In expansion, the pressure goes …
up
down
In reversible adiabatic expansion,
the pressure goes down
In reversible isothermal expansion …
the gas gets cold, so to keep it isothermal (at the same temperature), we add heat from the low temperature source, Ql
In reversible adiabatic compression, …
the pressure increases and we go from a “cold” isotherm to a “hot” isotherm
In reversible isothermal compression, …
the gas heats up, causing the pressure to go up, and to remain isothermal (at the same temperature), we must eject heat
Draw the Carnot refrigerator/heat pump cycle on a P-v diagram.
1 ↗ Qh
\ ↖ Th
\ 4
\ \ (slightly curved inwards in the center)
2→(Tl) 3
↑ QlWhat is the coefficient of performance (COP) for a reversible heat pump cycle?
A ratio of required work to useful heat
```
COPr)rev = 1/(Th/Tl -1
(COPhp)rev = 1/(1 - Tl/Th)
~~~
Higher COP mean …
low COP mean ….
high efficiency
low efficiency
Coefficients of performance is used for heat engines.
FALSE!
Thermal efficiency, η is for heat engines
COP are for heat pumps/refrigerators
Heat pumps and refrigerators work the same way, so what is the difference between a heat pump and a refrigerator?
Heat pumps are a reverse refrigerator. They warm buildings by pumping heat from outside (where it’s cold; normally winter) into a building (where it is hot).
Refrigerators take heat from food (where the environment is cold) and ejects that heat to surroundings outside the fridge (where it’s hot)
True or False;
(COP)rev < (COP)irr
(COP)rev > (COP)irr
Coefficients of performance, COP, are the best performance we can achieve with a heat pump or refrigerator.
True
