One of the most efficient heat engines ever built is a coal-fired steam turbine in the Ohio River valley, operating between 1870 0 C and 430 0 C. (a) What is its maximum theoretical efficiency? (b) The actual efficiency of the engine is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.40×10 5 J of energy each second from its hot reservoir?

Respuesta :

The engine's mechanical output is 88 * 104 W, and its theoretical maximum efficiency is 67.2%.

What benefits do coal-fired systems offer?

It's a dependable fuel; coal is a predictable, reliable, and dependable fuel as compared to solar or wind power. Despite not being at the vanguard of the country's energy output, it may offer a priceless backup service and a very dependable fuel for home stoves.

Briefing:

(a). The efficiency of a Carnot cycle linked with the same two reservoirs, as determined by Equation, is the appropriate level efficiency of this engine.

[tex]$\mathrm{e}_{\mathrm{C}}=1-\frac{\mathrm{T}_{\mathrm{c}}}{\mathrm{T}_{\mathrm{h}}}$[/tex]

Substitute numerical values:

[tex]$\mathrm{e}_{\mathrm{C}}=1-\frac{703.15}{2143.15}$[/tex]

= 0.672 = 67.2%

(b). Equation provides the engine's output power.

[tex]$\mathrm{P}=\frac{\mathrm{W}_{\text {eng }}}{\Delta \mathrm{t}}$[/tex]

Substitute for   [tex]$W_{\text {en }}$[/tex]  from Equation :

[tex]$\mathrm{P}=\frac{\mathrm{c}\left|\mathrm{Q}_{\mathrm{h}}\right|}{\Delta \mathrm{t}}$[/tex]

Substitute numerical values:

P = (0.42) (1.4 * 10⁵) / 1

  = 88 * 10⁴ W

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