(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

An ideal gas engine that works according to the following cycle.

Find the efficiency of this engine assuming that the heat capacities of the gas may be taken to be constant. Recall that the efficiency may be defined as:

[tex] \eta = \frac{Net work done over full cycle}{Heat absorbed along an isotherm} [/tex]

Express your answer in terms of the volumes [tex]V_1[/tex] and [tex]V_2[/tex] and the pressures [tex]P_1[/tex] and [tex]P_2[/tex] and the heat capacities at constant pressure and volume [tex]C_p[/tex] and [tex]C_v[/tex].

2. Relevant equations

[tex]W = \int P dV [/tex]

[tex]P V = N kB T [/tex]

[tex]C_v = 3N k_b /2 [/tex]

[tex]C_p = 5N k_b /2 [/tex]

3. The attempt at a solution

[tex] \eta = \frac{W}{Q} = \frac {W_a + W_b + W_c}{Q_c} [/tex]

[tex] W_a = P_2 (V_2 - V_1) [/tex]

[tex] W_b = 0 [/tex]

[tex] W_c = \int^{V_1}_{V_2} P dV = \int^{V_1}_{V_2} \frac{N k_b T}{V} dV = N k_b T ln (V_1 / V_2)[/tex]

To find [tex]Q_c[/tex], recall [tex]U = Q + W[/tex] and [tex]U=(3/2)N k_b T[/tex] which is constant on an isotherm. So [tex]Q_c=-W_c= -N k_b T ln (V_1 / V_2) [/tex]

Thus, by the equation of the efficiency,

[tex]\eta = \frac{N k_b T ln (V_1 / V_2)+P_2 (V_2 - V_1)}{-P_2 (V_2 - V_1)}[/tex]

However, I'm not sure if all my assumptions above are valid, and I don't see how the above could be put in terms of [tex]C_v[/tex] and [tex]C_p[/tex], since there's no relation between them and the temperature.

Any help is appreciated.

(So you know, I'm studying for a qualification exam this fall in graduate school. These problems are from past exams that they've given us to help study. I've been out of the physics world for a year and a half, so this stuff comes back slowly sometimes. I appreciate everyone who has responded so far to my questions.)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Efficiency of a Heat Engine

**Physics Forums | Science Articles, Homework Help, Discussion**