MHS Physics Department AP Unit II C 2 Laws of Thermodynamics Ref: Chapter 12

MHS Physics Department 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.

MHS Physics Department 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.

MHS Physics Department 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

MHS Physics Department Heat Exchange

MHS Physics Department 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

MHS Physics Department 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 (C V = 12.5J/mol K, C p = 20.8 J/mol K) is brought from state a to state b along the path shown in the following P-V diagram

MHS Physics Department 1.5 x 10 5 Pa P V (x10 -3 m ab 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

MHS Physics Department 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 m 3 to 85 m 3 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 m 3. What is the work done?

MHS Physics Department 2 nd Law Thermodynamics Heat Engine (E.g. Internal combustion engine) are Cyclic Engines ΔU = 0. They have a hot reservoir (Q H ) and a cold reservoir (Q C ). Q net = -W = Q H – Q C. Efficiency = work out/work in = (Q H – Q C )/Q H = 1- Q C /Q H Efficiency is always less than one!!!!!!!

MHS Physics Department Carnot Engine Theoretically most efficient engine Since Q is proportional to absolute temperature Efficiency = work out/work in = (T H – T C )/T H = 1- (T C /T H )

MHS Physics Department Diagram of pressure and volume graph for Carnot Engine

MHS Physics Department 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

MHS Physics Department 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 10 5 Pa is cooled from 100 °C to 0 °C, at constant volume, what is the change in pressure?