Question

8. A refrigerator may be regarded as the inverse of a steam engine, in that work is performed in order to remove heat from a system. It may be regarded as a steam engine run in reverse (i.e. the first step is a reversible adiabatic expansion from Th to Tc.) Heat is removed from the gas at the lower temperature in the succeeding isothermal expansion. The efficiency of a refrigerator is: Er = Aqoutput /Awinput Assuming a refrigerator can be built using a reversible Carnot cycle of a van der Waals gas, find an expression for the efficiency er: If Es is the efficiency of a Carnot steam engine, what is its relationship to Er? {i.e. find a relationship between er and es} Let Tc = 2TH. Find the value of 2 that maximizes the efficiency. What is the maximum value of er? Can a temperature of absolute zero be achieved by repeating the cycle with temperature lowered by the maximum efficiency each cycle? Explain using part c.

Answer 1

Part (b)

Relation between (n) and (B): T 1. β =- Τ, > T, T, -T, 1 Τ, Υ, Τ, η Τ, - Τ, η Τ, - Τ, Τ, 2, Τ, - Τ ' 1- η Τ, - Τ, +1 η Τ, -T, T T, -T, Again. n =