Correct Answer - Option 3 : 373 °C
CONCEPT:
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Carnot engine: The theoretical engine which works on the Carnot cycle is called a Carnot engine.
- It gives the maximum possible efficiency among all types of heat engines.
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Heat source: The part of the Carnot engine which provides heat to the engine is called a heat source.
- The temperature of the source is maximum among all the parts.
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Heat sink: The part of the Carnot engine in which an extra amount of heat is rejected by the engine is called a heat sink.
- The amount of work that is done by the engine is called work done.
The efficiency (η)of a Carnot engine is given by:
\(η = 1 - \frac{{{T_C}}}{{{T_H}}} = \;\frac{{Work\;done\left( W \right)}}{{{Q_{in}}}} = \;\frac{{{Q_{in}} - \;{Q_R}}}{{{Q_{in}}}}\)
Where TC is the temperature of the sink, TH is the temperature of the source, W is work done by the engine, Qin is the heat given to the engine/heat input and QRis heat rejected.
The relation between the Kelvin scale (K) and the celsius scale (°C);
K = °C + 273
CALCULATION:
Given that:
η = 50 % = 0.5
Heat sink temperature (TC) = 50 °C = 273 + 50 = 323 K
Heat source temperature (T H) = ?
\(η = 1 - \frac{{{T_C}}}{{{T_H}}} \)
\(0.5 = 1 - \frac{{{323}}}{{{T_H}}} \)
323/TH = 0.5
TH = 323/0.5 = 646 K = 646 - 273 = 373 °C
Hence option 3 is correct.
