Determine how high the combustion of 1.000 mol of CO could lift a 1.00 kg mass near the surface of the earth

Question

Carbon monoxide is used as the fuel for a Carnot engine with a high temperature of 450 o C and a cool temperature of 100 o C. Determine how high the combustion of 1.000 mol of CO could lift a 1.00 kg mass near the surface of the earth. Assume that all of the heat from the combustion is transferred to the engine and assume that the combustion takes place at 450 o C.

Answer 1

The efficiency of a Carnot engine is given by (T_hot - T_cold ) / T_hot . This is equal to the ratio of the maximum work obtainable from the heat transferred from the hot reservoir.

(T_hot - T_cold ) / T_hot = W_max / Q where Q is the heat obtained from the combustion of 1.00 mole if CO. From the internet, I found a value of 283 kj / mole for the combustion if one mole of CO = Q.

W_max = (723 - 273) / 723 x 283 kj = 176.1 kj.

The height to which a one kg mass can be lifted is h = W_max / 1.00 kg x 9.8 m/s².

h = 176.1 x 10³ j / 1.00 kg x 9.8m/s² = 17969 m. approximately as I used g to two sig figs.

Please check all calculations.