=4 moles of an ideal monatomic gas, with a ratio of heat capacities 1.67, initia

Question

=4 moles of an ideal monatomic gas, with a ratio of heat capacities 1.67, initially have a pressure p1=2atm, volume v=45L and a temperature t1. Then the gas undergoes the following three step cyclic process.

i) adibatic expanion form the temperature t1, pressure p1, and volume v1 to a temperature t2, volume v2=65L and pressure p2

ii) increase in pressure at constant volume to a pressure p3 and temperature t3

iii) isothermal compression to the original starting pressure, volume, and temperature.

a) what is t1

b) waht is t2 and p2

c) what are t3 and p3

d) what is the work done by the gas during each of the three steps of the cycel? What is the net work done by the gas during the entire cycle?

e)how much heat is absorbed by the gas during each of the three steps of the cycle? What is the net heat absorbed by the gas during the entire cycle? Why should this last result be exactlly the same as the last result in part d?

Explanation / Answer

A) t1 = 10^5 * .045 / (4*8.314) = 135.31K

B) p1 v1^1.67 = p2 * v2^1.67

p2 = 2*(45/65)^1.67 = 1.08 atm

t2 = 1.08*10^5 * .065 / (4*8.314) = 211.1 K

C) v3 = .065, p3 = 1.08*135.1/211.1 = 0.691 atm t3 = 135.1 K

D) i) -4*8.314*(135.31-211.1)/0.67 = 3762J ii) w23 = 0 III) w31 = 4*8.314*135.1 * ln( 45/65)) = -1652 J

wnet = 1110J

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