Laws of Thermodynamics
The Three Laws of Thermodynamics
- The first lawof thermodynamics, also called conservation of energy. We can use this
knowledge to determine the amount of energy in a system, the amount lost as waste
heat, and the efficiency of the system.
-The second lawof thermodynamics states that the disorder in the universe always
increases. As the disorder in the universe increases, the energy is transformed into
less usable forms. Thus, the efficiency of any process will always be less than 100%.
- The third law of thermodynamics tells us that all molecular movement stops at a
temperature we call absolute zero, or 0 Kelvin (-273oC). Since temperature is a
measure of molecular movement, there can be no temperature lower than absolute
zero. At this temperature, a perfect crystal has no disorder.
ENTROPY
Entropy a measure of the disorder of a
system.The concept of entropy addresses
the transformation of energy, and tells us
how much energy can be converted from
one form into another, and in particular,
how much energy is available for doing
useful work.
It is impossible to construct a heat engine
that performs an amount of work equal to
the heat absorbed by the system!
The entropy of the universe increases in all
natural processes.
ENTROPY
The change in entropy of a system, ΔS, is equal to the heat, ΔQ, flowing into the
system as it changes from one state to another divided by absolute temperature.
ENTROPY
The second law of thermodynamics enables us to classify all the processes under
two main categories: reversible (or ideal processes) and irreversible (or natural
processes).
REVERSIBLE PROCESS - The process in which the system and surroundings can be
restored to the initial state from the final state without producing any changes in
the thermodynamics properties.
IRREVERSIBLE PROCESS–
•the initial state of the system and surroundings cannot be restored from the
final state
•the various states of the system on the path of change from initial state to final
state are not in equilibrium with each other.
•the entropy of the system increases decisively and it cannot be reduced back to
its initial value.
ENTROPY
In a reversible process, ΔS remains constant
In a irreversible process, ΔS increases due to loss of energy (through friction,
leakage, damping, etc.)
ΔS = ΔQ/T
ΔS - positive when disorder increases or order decreases
ΔQ - heat exchange between system and surroundings (=0 in adiabatic process)
The Gasoline Engine
A gas engine means an engine running on a gas (any type of gas: bio fuel,
petroleum, natural gas, etc.).
Otto Cycle - Gasoline Engine
The process for a four-stroke gasoline engine is modeled using the Otto cycle.
(1) Air drawn into system (O to A). Volume
increases from V2to V1.
(2) From A to B: (compression stroke)
Air-fuel mixture is compressed from V1 to V2
adiabatically (w/o heat being transferred to the
surroundings). Temp increases from T1 to T2. Work
done on system.
(3) From B to C: (Qh, heat flows in due to
combustion). Both temp and pressure rise rapidly
but volume remains constant. No work done.
(4) From C to D: (power stroke) Gas expands
adiabatically. Volume increases from V2 to V1,
causing temp to fall. Work is done by system.
(5) From D to A: (Qc, heat extracted from system;
hot gas replaced by cool gas) Pressure falls at
constant volume. No work done.
(6) Exhaust stroke A to O.
Residual gases expelled. Volume
decreases from V1 to V2. Cycle
complete.
Engine Efficiency
Modern gasoline engines have max. thermal efficiencies of 25-30% when used to
power a car. Even when the engine is operating at its point of maximum
thermal efficiency about 70-75% is rejected as heat without being turned into
useful work. At idle, the thermal efficiency is zero since no usable work is being
drawn from the engine.
Engines using the Diesel cycle are usually more efficient, although the Diesel cycle
itself is less efficient at equal compression ratios. Diesel engines use much
higher compression ratios because the heat of compression is used to ignite the
slow-burning diesel fuel. The most efficient type, direct injection Diesels, are
able to reach an efficiency of about 40% in the engine speed range of idle to
about 1,800 rpm.
At high speeds, efficiency in both types of engine is reduced by pumping and
mechanical frictional losses, and the shorter time period within which
combustion has to take place.
Carnot Engine
The Carnot cycle is a theoretical thermodynamic cycle. It is the most efficient cycle
for converting a given amount of thermal energy into work, or conversely,
creating a temperature difference (e.g. refrigeration) by doing a given amount
of work.
A Carnot cycle acting as a heat
engine. The cycle takes place
between a hot reservoir at
temperature TH and a cold reservoir
at temperature TC.
It is not a practical engine cycle
because the heat transfer into the
engine in the isothermal process is
too slow to be of practical value. As
Schroeder puts it "So don't bother
installing a Carnot engine in your
car; while it would increase your gas
mileage, you would be passed on
the highway by pedestrians."
Carnot Cycle
1 to 2: Reversible isothermal expansion of the gas at the "hot"
temperature, TH (isothermal heat addition or absorption). During this
step (A to B on T-S diagram, 1 to 2 P-V diagram) the expanding gas makes
the piston work on the surroundings. The gas expansion is propelled by
absorption of quantity Q1 of heat from the high temperature reservoir.
Carnot Cycle
2 to 3: Reversible adiabaticexpansion of the gas.For this step (B to C on
T-S diagram, 2 to 3 on P-V diagram) the piston and cylinder are assumed
to be thermally insulated, thus they neither gain nor lose heat. The gas
continues to expand, working on the surroundings. The gas expansion
causes it to cool to the "cold" temperature, TC.
Carnot Cycle
3 to 4: Reversible isothermal compression of the gas at the "cold"
temperature, TC. (isothermal heat rejection) (C to D on T-S diagram, 3 to
4 on P-V diagram). Now the surroundings do work on the gas, causing
quantity Q2 of heat to flow out of the gas to the low temperature
reservoir.
Carnot Cycle
4 to 1: Reversible adiabaticcompression of the.(D to A on T-S diagram, 4
to 1 on P-V diagram) Once again the piston and cylinder are assumed to
be thermally insulated. During this step, the surroundings do work on the
gas, compressing it and causing the temperature to rise to TH. At this
point the gas is in the same state as at the start of step 1.
Carnot Cycle
Establishes upper limit on efficiency of all engines
Gives largest amount of work possible for a given amount of heat
supplied to system
All processes in the cycle are either adiabatic or isothermal and operate
in a reversible cycle (cycle where system & surroundings return to initial
state)
Adiabatic – complete combustion of fuel; no lingering ΔQ input in other
parts of cycle (no exchange of heat with surroundings)
Isothermal – no heat loss to walls; no turbulence of fluids; no friction; heat
transfer is done VERY slowly in order to retain isothermal quality
Carnot Efficiency
(Temp in Kelvins!)
Effc = 1 – Tc/Th
Example 13.29
In each cycle, a heat engine absorbs 375 J of heat and performs 25 J of
work.
(a) Find the efficiency of the engine
Example 13.29
In each cycle, a heat engine absorbs 375 J of heat and performs 25 J of
work.
(b) Find the heat expelled in each cycle
Example 13.37
The exhaust temperature of a Carnot heat engine is 300°C. What is the
intake temperature if the efficiency of the engine is 30%?
Example 13.47
An ice tray contains 500g of water at 0°C. Calculate the entropy change
of the water as it freezes completely and slowly at 0°C.