SATHEE: Thermodynamics - Result Question 49

Thermodynamics - Result Question 49

51. A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} C$ , the efficiency of the engine is doubled. The temperatures of the source and sink are

[2000]

(a) $99^{\circ} C, 37^{\circ} C$

(b) $80^{\circ} C, 37^{\circ} C$

(d) $90^{\circ} C, 37^{\circ} C$

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Answer:

Correct Answer: 51. (a)

Solution:

(a) Initially the efficiency of the engine was $\frac{1}{6}$ which increases to $\frac{1}{3}$ when the sink temperature reduces by $62^{\circ} C$ .

$η = \frac{1}{6} = 1 - \frac{T_{2}}{T_{1}}$ , when $T_{2} =$ sink temperature

$T_{1}$ source temperature $\Rightarrow T_{2} = \frac{5}{6} T_{1}$

Secondly,

$\frac{1}{3} = 1 - \frac{T_{2} - 62}{T_{1}} = 1 - \frac{T_{2}}{T_{1}} + \frac{62}{T_{1}} = 1 - \frac{5}{6} + \frac{62}{T_{1}}$

or, $T_{1} = 62 \times 6 = 372 K = 372 - 273 = 99^{\circ} C$

$Misplaced &$

52 .

(d) $η = 1 - \frac{T_{1}}{T_{2}}$

$T_{1} = - 23^{\circ} C = 250 K, T_{2} = 100^{\circ} C = 373 K$

$η = 1 - \frac{250}{373} = \frac{373 - 250}{373}$

Thermodynamics - Result Question 49

51. A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} C$ , the efficiency of the engine is doubled. The temperatures of the source and sink are

Answer:

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Thermodynamics - Result Question 49

51. A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by 62∘C, the efficiency of the engine is doubled. The temperatures of the source and sink are

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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51. A reversible engine converts one-sixth of the heat input into work. When the temperature of the sink is reduced by $62^{\circ} C$ , the efficiency of the engine is doubled. The temperatures of the source and sink are