To improve the efficiency of a Carnot engine, you can increase the difference in temperature between its cold and hot reservoir.  You have a Carnot engine that usually operates between 710.5 K (hot) and 444.5 K (cold).  You can apply a change of temperature of 42 K to either the hot (710.5+42, case 1) or the cold (444.5-42, case 2).  Calculate the ratio in efficiencies: e(case1) / e(case2)

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