What are the differences between isothermal expansion and adiabatic expansion?
Heat and work are means of transferring energy to and from a system, and internal energy—the energy of molecular motion—varies as heat and work are added to or removed from a system. Thermodynamics is the study of heat and work.
Q: Heat (in calories); W: Work (in Joules); U: Internal Energy (actually, internal motion of molecules); Note: 1000 Cal = 4186 Joules.
First Thermodynamic Law
U = Q - W The first law applies specifically to isothermal and adiabatic systems.
ISOTHERMAL: Since there is no temperature change during a thermodynamic exchange, U = 0. As a result, Q = W is the result of the First Law.
Heat and work are interchangeable in this situation.
Imagine an emphysema sufferer blowing up a balloon very, very slowly. This is a good example of an isothermal exchange because the balloon expands so slowly that there is no change in temperature and the internal energy remains constant—it's like watching paint dry.
ADIABATIC: Since there is no change in heat during a thermodynamic exchange, Q = 0. As a result, U = -W becomes the First Law.
Here, internal energy is solely dependent on work. The corresponding equations can be complex. To prevent ambiguity (and incorrect test answers), follow these steps:
(1) U = - (+W) Internal energy is negative because work is being done on the environment by the system, which is a positive equation.
(2) U = - (-W) Internal energy is positive in this equation because work is negative and is being done ON the system by the environment.
A balloon connected to a helium pump and QUICKLY blown up is a good example of an adiabatic exchange because the heat is faked out and doesn't have time to react; it's like, "Whoa, dude, what just happened?"
A third kind of thermodynamic system is ISOVOLUMETRIC, in which W = 0 since there isn't any volume change during a thermodynamic exchange.
When W = 0, the First Law reduces to U = Q. Work is equivalent to Pressue x change in Volume (W = PdeltaV), so no change in volume indicates no work is done.
Here, internal energy is solely dependent on heat; reactions in rigid containers, where volume changes are not possible, are typical examples. If heat is added to a system, Q is positive and internal energy increases; if heat is removed from the system, Q is negative and internal energy decreases.
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Isothermal expansion occurs at a constant temperature, while adiabatic expansion occurs without the transfer of heat. Additionally, in isothermal expansion, the internal energy remains constant, while in adiabatic expansion, the change in internal energy is dependent on the work done by or on the system. Lastly, the pressure and volume relationship in isothermal expansion follows Boyle's Law (PV = constant), while in adiabatic expansion, it follows a different equation (PV^γ = constant, where γ is the adiabatic index).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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- One #"mol"# of an ideal gas, initially at #"300 K"#, is cooled at constant #"V"# so that #"P"_f# is #1/4 "P"_i#. Then the gas expands at constant #"P"# until it reaches #"T"_i# again. What is the work #w# done on the gas?
- A #6 L# container holds #5 # mol and #6 # mol of gasses A and B, respectively. Groups of three of molecules of gas B bind to two molecules of gas A and the reaction changes the temperature from #480^oK# to #270^oK#. How much does the pressure change?
- How does heat affect pressure?

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