The temperature­- entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

  • Option 1)

    1/3\;

  • Option 2)

    \; 2/3\;

  • Option 3)

    \; 1/2\;

  • Option 4)

    \; 1/4

 

Answers (1)

As we learnt in 

Entropy -

It is a measure of disorder of molecular motion of a system.

- wherein

Greater is disorder greater is entropy

dS= \frac{dQ}{T}

and 

Efficiency of a cyclic process -

\eta = \frac{work\, done \, per \, cyclic}{gross \, heat\, supplied \, per\, cyclic}

 

- wherein

Gross heat implied only part of heat absorbed.

 

The efficiency of cycle is:

n = \frac{work\ done}{heat\ absorb}

= \frac{Q_{1}-Q_{2}}{Q_{1}}

= \frac{Area\ of\ cycle}{Area\ under\ AB\ curve}

Efficiency \eta = \frac{\frac{1}{2}\times T_{0}\times S_{0}}{T_{0}S_{0}+\frac{1}{2}T_{0}S_{0}}= \frac{1}{3}

 

 

 


Option 1)

1/3\;

This option is correct.

Option 2)

\; 2/3\;

This option is incorrect.

Option 3)

\; 1/2\;

This option is incorrect.

Option 4)

\; 1/4

This option is incorrect.

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