Chapter 19. “A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended.

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Presentation transcript:

Chapter 19

“A theory is the more impressive the greater the simplicity of its premises, the more different kinds of things it relates, and the more extended its area of applicability. Therefore the deep impression that classical thermodynamics made upon me. It is the only physical theory of universal content which I am convinced will never be overthrown, within the framework of applicability of its basic concepts.” A. Einstein

An monatomic ideal gas moves from state A to state B along the straight line shown. In which case is the change in internal energy of the system the biggest? 1. Case 1 2. Case 2 3. Same A B V(m 3 ) Case 1 A B V(m 3 ) P(atm) Case 2 P(atm)

A B V(m 3 ) Case 1 A B V(m 3 ) P(atm) Case 2 P(atm)

Heat is the amount energy transfer due to a temperature difference. All other forms of energy transfer are classified as work. In the picture below, heat is flowing from the hot object to the cold object.

Q : Heat going into the system W : Work done by the system

(Work done by the system) = (−1) × (Work done on the system) (Heat going into the system) = (−1) × (Heat going out of the system) W = +100J Work done by the system = +100J Work done on the system = -100J W = -150J Work done by the system = -150J Work done on the system = +150J Q = +100J Heat going into the system = +100J Heat going out of the system = -100J Q = -150J Heat going into the system = -150J Heat going out of the system = +150J

ΔU = Q - W Work done by system When work done by the system is positive, the system loses energy. When work done by the system is negative, the system gains energy. Heat going into system Increase in internal energy U, Q, W are all in J.

If all the signs seems confusing, simply remember this: Expansion  W >0 Compression  W <0

The work in each case is different, so you must be careful when calculating W.

A system moves from state A to state B along the straight line shown. In which case is the work done by the system the biggest? 1. Case 1 2. Case 2 3. Same A B V(m 3 ) Case 1 A B V(m 3 ) P(atm) Case 2 P(atm)

V P W = PΔV V P W = ΔV = 0 V P PV = const W Isobaric: constant pressure Isochoric: constant volume Isothermal: constant temperature Adiabatic: no heat exchange Q =0

We used:

Imagine that an ideal monatomic gas is taken from its initial state A to state B by an isothermal process, from B to C by an isobaric process, and from C back to its initial state A by an isochoric process. Fill in the signs of Q, W, and ΔU for each step. StepQWΔU A  B B  C C  A V (m 3 ) P (atm) A B C

VP1 2 V 1 V 2 P N molecules of ideal gas is taken from state 1 to state 2 at constant pressure P, from V 1 to V 2. Find T 1, T 2, ΔU, W, Q in terms of N, P, V 1, V 2.

A process is cyclic if after one cycle the system returns to the starting point. For a cyclic process, after one complete cycle, ΔU=0, but Q and W may not be zero.

W(A  B) = W(B  C) = 0 W(C  A) = − W(A  B  C  A) = = = +12kJ

Adiabatic processes obey the following relation:

adiabatically A box of monatomic gas at pressure 1atm is compressed from 6m 3 to 2m 3 adiabatically, find the final pressure. isothermalnot adiabatic What if the compression is isothermal but not adiabatic?

By definition Q=0 for adiabatic processes. To find W, one can simply apply the First Law: