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LECTURE 12 FIRST LAW OF THERMODYNAMICS Lecture instructor: Kazumi Tolich Lecture 12

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¨ Reading chapter 15-1 to 15-2 ¤ First law of thermodynamics ¤ Work n Work and the PV diagram for a gas ¤ Thermal processes n Constant pressure n Constant volume n Isothermal n Adiabatic First law of thermodynamics

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¨ The first law of thermodynamics is a statement of the conservation of energy.

¨ The change in a system’s internal energy ΔU is related to the heat Q and the work W as follows: ΔU = Q −W Internal energy vs. heat and work

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¨ The state of a system is determined by its temperature, pressure, and volume. It is an intrinsic property of a system.

¨ The internal energy of the system depends only on the state of the system, its temperature, so the internal energy is a state function.

¨ The work done and the heat added, however, depend on the details of the process involved, so they are not state functions.

¨ We cannot say that a system “contains” a certain amount of heat or work. Example: 1

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¨ One mole of an ideal monoatomic gas is initially at a temperature of Ti = 283 K. a) Find the final temperature of the gas, Tf, if Q = 3280 J of heat is added to it, and it does W = 722 J of work. b) Suppose the amount of the gas is doubled. Does Tf in a) increase, decrease, or stay the same? Thermal process assumptions

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¨ All thermal processes are quasi-static.

¤ They are slow enough that the system is always in equilibrium.

¤ The pressure and temperature are uniform throughout the system.

¨ All thermal processes are reversible.

¤ For a process to be reversible, it must be possible to return both the system and its surroundings to exactly the same states in which they were before the process began. Irreversible processes

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¨ Examples of irreversible (not reversible) processes: ¤ Friction between a piston and the cylinder generate heat that escapes the cylinder. ¤ A process occurs rapidly to cause turbulence. ¤ A process occurs rapidly without being in equilibrium.

¨ In practice, all real processes are irreversible, but we can approximate many processes with a reversible process. Work and PV plot

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¨ The work done by an expanding gas is equal to the area under the curve representing the process in a pressure vs. volume plot (PV plot).

¨ The area under the curve is negative if ΔV is negative. Clicker question: 1

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¨ In a process under a constant pressure P, work done by an expanding gas W as the volume of the gas changes by ΔV is given by W = PΔV Example: 2

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¨ An ideal gas is compressed at constant pressure to one- half its original volume. If the pressure of the gas is P = 120 kPa, and 760 J of work is done on it, find the initial volume of the gas. Constant volume process

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¨ In a constant-volume process, nothing moves, and no work is done on the surrounding. W = 0 Isothermal process

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¨ In an isothermal process, the temperature T is constant.

¨ From the equation of state for an ideal gas, you see that PV = NkT = nRT = constant.

¨ The pressure varies inversely with the volume.

¨ The work done by an expanding gas is given by

!V $ !V $ W = NkT ln# f & = nRT ln# f & "Vi % "Vi % Example: 3

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¨ Suppose n = 145 moles of a monoatomic ideal gas undergo an isothermal expansion 3 3 from Vi = 1.00 m to Vf = 4.00 m . a) What is the temperature at the beginning and at the end of this process?

b) How much work is done by the gas during this expansion? Adiabatic process

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¨ An adiabatic process is one in which no heat flows into or out of the system, Q = 0.

¨ The adiabatic PV curve is similar to the isothermal one, but is steeper.

¨ Adiabatic process can be created by the following:

¤ Thermally insulate the system

¤ Have the volume change occur very quickly so that the heat has no time to flow in or out of the system.

¨ Since ΔU = Q − W, the work done by the gas is given by W = −ΔU Example: 4

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¨ During an adiabatic process, the temperature of a monoatomic ideal gas drops

from Ti = 495 °C to Tf = 215 °C . If the gas does W = 19.2 kJ of work, how many moles of molecules are there is the gas? Demo: 1

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¨ Fire syringe

¨ Temperature change with compression ¤ Demonstration of adiabatic process n Rapid compression causing temperature to raise. Summary

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¨ Various thermodynamic processes and their characteristics Clicker question: 2

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