WRONG

WRONG

atmospheric pressure of environment does “free”work on system, or system does work to displaceatmospheric gas as it expands (this work is ‘lost’).

is the extra work of an isobaric process

is the extra work of an isobaric process

Problem 8.3 K&K: Photon Carnot engine. Consider a Carnot engine that uses as the working substance a photon gas.

(a) Given h and l as well as V1 and V2, determine V3 and V4.

(b) What is the heat Qh taken up and the work done by the gas during the first isothermal expansion? Are they equal to each other, as for the ideal gas?

(c) Do the two isentropic stages cancel each other, as for the ideal gas?

(d) Calculate the total work done by the gas during one cycle. Compare it with the heat taken up at h and show that the energy conversion efficiency is the Carnot efficiency.

1st, identify the two aspects of our knowledge the problem requires :

1. what do we know about a Photon gas? 2. What do we know about Carnot engines?

Photon gas:

U/V = [2/(15h3c3)]4 or U = cV4

= [(42V)/45][/(hc)]3 = c’V3

P = U/3V = (c/3)4 (U has units of volume …P independent of V, unlikeideal gas: P= N/V)

1st, identify the two aspects of our knowledge the problem requires :

1. what do we know about a Photon gas? 2. What do we know aboutCarnot engines?

Photon gas:

U/V = [2/(15h3c3)]4 or U = cV4

= [(42V)/45][/(hc)]3 = c’V3

P = U/3V = (c/3)4 (U has units of volume …P independent of V, unlikeideal gas: P= N/V)

1st, identify the two aspects of our knowledge the problem requires :

1. what do we know about a Photon gas? 2. What do we know aboutCarnot engines?

Photon gas:

U/V = [2/(15h3c3)]4 or U = cV4

= [(42V)/45][/(hc)]3 = c’V3

P = U/3V = (c/3)4 (U has units of volume …P independent of V, unlikeideal gas: P= N/V)

Carnot engine: cyclic process has four stages, two isothermaland two isentropic (adiabatic).

For an ideal gas:

How does PVdiagram differ forA photon gas?

(a) Given h and l as well as V1 and V2, determine V3 and V4.

We know 2 = 3 and 1 = 4

V2h3 = V3l

3 V1h3 = V4l

3

So, V3 = (h/l)3V2 V4 = (h/l)3V1

(b) What is the heat Qh taken up and the work done by the gas during the first isothermal expansion? Are they equal to each other, as for the ideal gas?

For the isothermal stage of an ideal gas: U1to2= 0Thus,U1to2 = Q1to2 – W1to2 = 0

Q1to2 = W1to2.

(using convention W by is -, heat in is +)

For a photon gas:

(c) Do the two isentropic stages cancel each other, as for the ideal gas?

(d) Calculate the total work done by the gas during one cycle. Compare it with the heat taken up at h and show that the energy conversion efficiency is the Carnot efficiency.