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Who represented (invented) carnot engine...

Who represented (invented) carnot engine at first ?

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The temperatures T_(1) and T(2) of two heat reservoirs in an ideal carnot engine are 1500^(@)C and 500^(@)C . Which of these (a) increasing T_(1) by 100^(@)C or (b) decreasing T_(2) by 100^(@)C would result in greater improvement of the efficiency of the engine?