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AP Unit II C 2

Laws of Thermodynamics

Ref: Chapter 12

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• a) Students should know how to apply the first law of thermodynamics, so they can:

• (1) Relate the heat absorbed by a gas, the work performed by the gas, and the internal energy change of the gas for any of the processes above.

• (2) Relate the work performed by a gas in a cyclic process to the area enclosed by a curve on the PV diagram.

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• b) Students should understand the second law of thermodynamics, the concept of entropy and heat engines and the Carnot cycle, so they can:

• (1) Determine whether entropy will increase, decrease, or remain the same during a particular situation.

• (2) Compute the maximum possible efficiency of a heat engine operating between two given temperatures.

• (3) Compute the actual efficiency of a heat engine.• (4) Relate the heats exchanged at each thermal

reservoir in a Carnot cycle to the temperatures of the reservoirs.

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1st Law of thermodynamics.

• This is a statement of the conservation of energy.• An insulated container filled with an ideal gas

rests on a heat reservoir. The container is fitted with a snug but frictionless weighted piston that can be raised or lowered. The confined gas is the system and the piston and heat reservoir are the surroundings

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Heat Exchange

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• Work is done on the system when the gas is compressed. W = - F Δs.

• Since F = PA and A Δs = V we have • W = -P ΔV• and vice versa.• W is negative when the system does work against its

surroundings, and positive when the surroundings do work on the system

• isochoric - constant volume, isobaric - constant pressure, isothermal - constant temperature, adiabatic - no heat exchanged

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First Law Thermodynamics

• The system’s internal energy ΔU = Q (heat energy) + W (work done on the gas)

• ΔU = Q + W

• A 0.5 mol of an ideal gas (CV = 12.5J/mol K, Cp = 20.8 J/mol K) is brought from state a to state b along the path shown in the following P-V diagram

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1.5 x 105 Pa

P

V (x10-3 m3

10

30

a b What are the values of each of the following (a) Temperature at a and b b) Work done by the gas during ab

c) Heat added to the gas during ab d) change in internal energy of gas

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1. R in Physics is 8.31 j/mol K. In chemistry they use J/liters K. If 1 mol of gas is 22.4 liters, what will be R in chemistry?

2. A gas expand from 4 m3 to 85 m3 at constant pressure of 1 atmosphere. How much work does it do.

3. A gas increases in pressure from 1 atmosphere to 3 atmospheres at a constant volume of 4 m3. What is the work done?

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2nd Law Thermodynamics

• Heat Engine (E.g. Internal combustion engine) are Cyclic Engines ΔU = 0. They have a hot reservoir (QH) and a cold reservoir (QC). Qnet = -W = QH – QC.

• Efficiency = work out/work in = (QH – QC)/QH = 1- QC/QH

Efficiency is always less than one!!!!!!!

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Carnot Engine

• Theoretically most efficient engine

• Since Q is proportional to absolute temperature

• Efficiency = work out/work in = (TH – TC)/TH = 1- (TC/TH)

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Diagram of pressure and volume graph for Carnot Engine

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Entropy• The change in entropy of a system (ΔS) is equal to the heat

flowing into or out of the system (ΔQ) divided by the absolute temperature (T). Entropy is a measure of the disorder of the universe. Reactions tend to go in the direction of increasing Entropy.

• ΔS = ΔQ/T• Therefore the second law of thermodynamics can be stated in

two ways:• 1. Heat will not flow spontaneously from a cold object to a hot

object.• 2. No heat engine operating in a cycle can absorb thermal

energy from a reservoir and perform an equal amount of work

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• 1. If the heat flowing into a system is 200 Joules at 373K, what is the entropy of the system?

• 2. If the Carnot internal combustion engine operates at 800°C and exhausts to 25 °C , what is the theoretical efficiency of the engine?

• 3. If 330 ml of steam at 1 x 105 Pa is cooled from 100 °C to 0 °C, at constant volume, what is the change in pressure?