A Carnot engine has an efficiency of <math> <mn>50</mn> <mi mathvariant="normal">%</mi> </math> when its source is at a temperature <math> <msup> <mrow> <mrow> <mn>327</mn> </mrow> </mrow> <mrow> <mrow> <mo>?</mo> </mrow> </mrow> </msup> <mi mathvariant="normal">C</mi> </math> . The temperature of the sink is:

T i = - 50 ? C  = 223 K V r m s ∝ T As v r m s increased by 3 timesSo v r m s f = 4 v r m s initial  T f = 16 T i  = 16 × 223  = 3568 K T f = ( 3568 - 273 ) ? C  = 3295 ? C (c) Fundamental harmonic frequency open pipe = V 2 L = v 1 (say)Fundamental harmonic frequency of closed pipe = V 4 L  = v 2 (say) ⇒ v 1 v 2 = V 2 L V 4 L 2 : 1

A Carnot engine has an efficiency of <math> <mn>50</mn> <mi mathvariant="normal">%</mi> </math> when its source is at a temperature <math> <msup> <mrow> <mrow> <mn>327</mn> </mrow> </mrow> <mrow> <mrow> <mo>?</mo> </mrow> </mrow> </msup> <mi mathvariant="normal">C</mi> </math> . The temperature of the sink is: &lt;!-- [if !supportLineBreakNewLine]--&gt; &lt;!--[endif]--&gt;

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Physics Thermodynamics Physics Class 11th Thermodynamics

A Carnot engine has an efficiency of $50 %$ when its source is at a temperature $327^{?} C$ . The temperature of the sink is:

Option 1 -

$200^{\circ} C$

Option 2 -

$27^{\circ} C$

Option 3 -

$15^{\circ} C$

Option 4 -

$100^{\circ} C$

4 Views | Posted a month ago

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1 Answer

Answered by

alok kumar singh | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

$T i = - 50^{?} C$

$\begin{array}{r} = 223 K \\ V_{r m s} \propto \sqrt[]{T} \end{array}$

As $v_{r m s}$ increased by 3 times

So ${(v_{r m s})}_{f} = 4 {(v_{r m s})}_{initial}$

$T_{f} = 16 T_{i}$

$= 16 \times 223$

$= 3568 K$ $T_{f} = (3568 - 273)^{?} C$

$= 3295^{?} C$

$= \frac{V}{2 L} = v_{1}$

(say)

Fundamental harmonic frequency of closed pipe $= \frac{V}{4 L}$

$= v_{2}$ (say)

$\Rightarrow \frac{v_{1}}{v_{2}} = \frac{\frac{V}{2 L}}{\frac{V}{4 L}} 2 : 1$

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A Carnot engine has an efficiency of $50 %$ when its source is at a temperature $327^{?} C$ . The temperature of the sink is:

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A Carnot engine has an efficiency of 50 % when its source is at a temperature 327 ? C . The temperature of the sink is:

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A Carnot engine has an efficiency of $50 %$ when its source is at a temperature $327^{?} C$ . The temperature of the sink is: