One of the efficient heat engines ever built is a coal-fired steam turbine in the Ohio River valley, operating between 1 870^0C and 430^0C. (a) What is its maximum theoretical efficiency? (b) The actual efficiency of the engine is 42.0%. How much mechanic (2024)

Standard XI

Physics

Engines and Cycles

The maximum theoretical efficiency of this engine is the efficiency of a Carnot engine connected between the same two reservoirs, found from Equation

$$e_{\mathrm{C}}=1-\dfrac{T_{c}}{T_{h}}$$

Substitute numerical values:

$$e_{C} =1-\dfrac{703.15}{2143.15} $$

$$=0.672=67.2 \%$$

(b) The output power of the engine is found from Equation :

$$P=\dfrac{W_{\text {eng }}}{\Delta t}$$

Substitute for $$W_{\text {en }}$$ from Equation :

$$P=\dfrac{c\left|Q_{h}\right|}{\Delta t}$$

Substitute numerical values:

$$P =\dfrac{(0.42)\left(1.4 \times 10^{5}\right)}{1}$$

$$=88 \times 10^{4} \mathrm{W}$$

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