The efficiency of Carnot engine = _________.

SOLUTION

CONCEPT:

The efficiency of the Carnot cycle (η):

• It is defined as the ratio of net mechanical work done per cycle the gas (W) to the amount of heat energy absorbed per cycle from the source (Q1) i.e.,

\(\eta =\frac{W}{{{Q}_{1}}}~\)

As work done by the engine per cycle  is

⇒ W = Q1 – Q2

Where, Q1 = amount of heat energy absorbed per cycle from the source and Q2 = energy absorbed per cycle from the sink.

\(\Rightarrow \eta =\frac{{{Q}_{1}}-{{Q}_{2}}}{{{Q}_{1}}}=1-\frac{{{Q}_{2}}}{{{Q}_{1}}}\)

As \(\frac{{{Q}_{2}}}{{{Q}_{1}}}=\frac{{{T}_{2}}}{{{T}_{1}}}\)

\(\Rightarrow \eta =1-\frac{{{T}_{2}}}{{{T}_{1}}}\)

Where T1 = temperature of the source and T2 = temperature of the sink.

EXPLANATION:

• The efficiency of the Carnot engine:

\(\Rightarrow \eta =1-\frac{{{T}_{2}}}{{{T}_{1}}}\)

\( \Rightarrow \eta = 1 - \frac{{{\rm{Temperature\;of\;Sink}}}}{{{\rm{\;Temperature\;of\;source}}}}\)