1. Adiabatic Lapse Rates and the First Law of ThermodynamicsTo fully
understand diabatic and adiabatic processes, we refer to a version of
the first law of thermodynamics, which states what happens when heat is
added to or removed from gases. Specifically, if heat is added, there
will be some combination of an expansion of the gas and an increase in
its temperature. The law is given in numerical form as...where ΔH = heat
added to the system, p is the air pressure, Δα is the change in volume
(positive for expansion and negative for contraction), cv is the
specific heat for air (assuming a constant volume), and ΔT is the change
in temperature. (Note that the Greek letter delta, Δ, preceding a
symbol represents a change in the value of the quantity.) The first term
on the right-hand side of the equation, p • Δα, is the work performed
by the gas as expansion occurs. The second term, cv • ΔT, refers to the
change in internal energy. The important thing for us is that heat added
to the air does not simply disappear but rather is apportioned between
temperature and volume changes.The first law of thermodynamics describes
the underlying principle of what occurs in the cylinder of an internal
combustion engine in an automobile, as shown in Figure 5-5-1. As the
air-fuel mixture burns, it expands and pushes down on the piston (this
is the work performed) and ultimately propels the car. In addition,
there is an increase in the internal energy of the gas, which we observe
as an increase in temperature. (Just ask anyone who has ever burned a
hand on an exhaust manifold!) The energy unleashed with the combustion
of the fuel is therefore manifested as work performed and an increase in
temperature. Of course, good automotive design calls for the engine to
convert most of the chemical energy to work performed, with little going
toward an increase in internal energy. In other words, engine heat
represents wasted energy, and a cold exhaust manifold would be the mark
of good engineering. The same relationship among heat, temperature, and
volume applies to our atmosphere.An adiabatic process represents a
special case of the first law of thermodynamics in which the left-hand
side of the equation equals 0 (no heat is added or removed).
Substituting 0 for ΔH yields...which can be rearranged as...or...Stated
in words, the adiabatic form of the first law indicates that if no heat
is added or removed from the system, work performed by the air (the
expansion of the gas) causes a decrease in internal energy (a decrease
in temperature) and work performed on the gas (compression) leads to
warming. Stated even more succinctly, expanding air cools and air
undergoing compression warms.What is the first law of
thermodynamics?FIGURE 5-5-1 Car Engine as an Illustration of Adiabatic
Processes. A four-stroke automobile engine works on the principle
invoked by the first law of thermodynamics. As the piston is pulled down
by the crankshaft, (a) and (b), an air-fuel mixture enters the
cylinder. In the second stroke the mixture is compressed (c). The third
stroke occurs when the spark plug fires, causing combustion of the
air-gas mixture (d). The energy released by the burning fuel is
manifested as work done by the moving piston and an increase in internal
energy (the increase in temperature). The burned fuel is expelled
during the fourth stroke (e).... Get solution
2. Adiabatic Lapse Rates and the First Law of ThermodynamicsTo fully understand diabatic and adiabatic processes, we refer to a version of the first law of thermodynamics, which states what happens when heat is added to or removed from gases. Specifically, if heat is added, there will be some combination of an expansion of the gas and an increase in its temperature. The law is given in numerical form as...where ΔH = heat added to the system, p is the air pressure, Δα is the change in volume (positive for expansion and negative for contraction), cv is the specific heat for air (assuming a constant volume), and ΔT is the change in temperature. (Note that the Greek letter delta, Δ, preceding a symbol represents a change in the value of the quantity.) The first term on the right-hand side of the equation, p • Δα, is the work performed by the gas as expansion occurs. The second term, cv • ΔT, refers to the change in internal energy. The important thing for us is that heat added to the air does not simply disappear but rather is apportioned between temperature and volume changes.The first law of thermodynamics describes the underlying principle of what occurs in the cylinder of an internal combustion engine in an automobile, as shown in Figure 5-5-1. As the air-fuel mixture burns, it expands and pushes down on the piston (this is the work performed) and ultimately propels the car. In addition, there is an increase in the internal energy of the gas, which we observe as an increase in temperature. (Just ask anyone who has ever burned a hand on an exhaust manifold!) The energy unleashed with the combustion of the fuel is therefore manifested as work performed and an increase in temperature. Of course, good automotive design calls for the engine to convert most of the chemical energy to work performed, with little going toward an increase in internal energy. In other words, engine heat represents wasted energy, and a cold exhaust manifold would be the mark of good engineering. The same relationship among heat, temperature, and volume applies to our atmosphere.An adiabatic process represents a special case of the first law of thermodynamics in which the left-hand side of the equation equals 0 (no heat is added or removed). Substituting 0 for ΔH yields...which can be rearranged as...or...Stated in words, the adiabatic form of the first law indicates that if no heat is added or removed from the system, work performed by the air (the expansion of the gas) causes a decrease in internal energy (a decrease in temperature) and work performed on the gas (compression) leads to warming. Stated even more succinctly, expanding air cools and air undergoing compression warms.What changes in work performed and internal energy occur when a parcel of air is lifted?FIGURE 5-5-1 Car Engine as an Illustration of Adiabatic Processes. A four-stroke automobile engine works on the principle invoked by the first law of thermodynamics. As the piston is pulled down by the crankshaft, (a) and (b), an air-fuel mixture enters the cylinder. In the second stroke the mixture is compressed (c). The third stroke occurs when the spark plug fires, causing combustion of the air-gas mixture (d). The energy released by the burning fuel is manifested as work done by the moving piston and an increase in internal energy (the increase in temperature). The burned fuel is expelled during the fourth stroke (e).... Get solution
2. Adiabatic Lapse Rates and the First Law of ThermodynamicsTo fully understand diabatic and adiabatic processes, we refer to a version of the first law of thermodynamics, which states what happens when heat is added to or removed from gases. Specifically, if heat is added, there will be some combination of an expansion of the gas and an increase in its temperature. The law is given in numerical form as...where ΔH = heat added to the system, p is the air pressure, Δα is the change in volume (positive for expansion and negative for contraction), cv is the specific heat for air (assuming a constant volume), and ΔT is the change in temperature. (Note that the Greek letter delta, Δ, preceding a symbol represents a change in the value of the quantity.) The first term on the right-hand side of the equation, p • Δα, is the work performed by the gas as expansion occurs. The second term, cv • ΔT, refers to the change in internal energy. The important thing for us is that heat added to the air does not simply disappear but rather is apportioned between temperature and volume changes.The first law of thermodynamics describes the underlying principle of what occurs in the cylinder of an internal combustion engine in an automobile, as shown in Figure 5-5-1. As the air-fuel mixture burns, it expands and pushes down on the piston (this is the work performed) and ultimately propels the car. In addition, there is an increase in the internal energy of the gas, which we observe as an increase in temperature. (Just ask anyone who has ever burned a hand on an exhaust manifold!) The energy unleashed with the combustion of the fuel is therefore manifested as work performed and an increase in temperature. Of course, good automotive design calls for the engine to convert most of the chemical energy to work performed, with little going toward an increase in internal energy. In other words, engine heat represents wasted energy, and a cold exhaust manifold would be the mark of good engineering. The same relationship among heat, temperature, and volume applies to our atmosphere.An adiabatic process represents a special case of the first law of thermodynamics in which the left-hand side of the equation equals 0 (no heat is added or removed). Substituting 0 for ΔH yields...which can be rearranged as...or...Stated in words, the adiabatic form of the first law indicates that if no heat is added or removed from the system, work performed by the air (the expansion of the gas) causes a decrease in internal energy (a decrease in temperature) and work performed on the gas (compression) leads to warming. Stated even more succinctly, expanding air cools and air undergoing compression warms.What changes in work performed and internal energy occur when a parcel of air is lifted?FIGURE 5-5-1 Car Engine as an Illustration of Adiabatic Processes. A four-stroke automobile engine works on the principle invoked by the first law of thermodynamics. As the piston is pulled down by the crankshaft, (a) and (b), an air-fuel mixture enters the cylinder. In the second stroke the mixture is compressed (c). The third stroke occurs when the spark plug fires, causing combustion of the air-gas mixture (d). The energy released by the burning fuel is manifested as work done by the moving piston and an increase in internal energy (the increase in temperature). The burned fuel is expelled during the fourth stroke (e).... Get solution
