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 T_1 to T_3). Heat is removed from the gas at the lower temperature in the succeeding isothermal step. The efficiency of a refrigerator is e_r = (Heat out)/(Total work in) a) Assuming a refrigerator can be built using a reversible Carnot cycle of a van der Waals gas, find an expression for the efficiency e_r. b) If e_s is the efficiency of a Carnot steam engine, what is its relationship to er? (i. e. find a relationship between e_r and e_s} c) What is the efficiency needed to reduce the temperature of a system by a factor of 1/2? (i. e. show that the maximum possible ratio of lambda = T_3/T_1 is 1/2). d) Can a temperature of absolute zero be achieved by repeating the cycle with temperature lowered by 1/2 each cycle? Explain using part c. e) Which law of thermodynamics is violated if lambda > 1/2? Explain in 20 words or less.