Figure below represents a Carnot engine that works between temperatures T1 400 K

Question

Figure below represents a Carnot engine that works between temperatures

T_{1}

400 K and

T_{2}

150 K and drives aCarnot refrigerator that works between temperatures

T_{3}

325 K and

T_{4}

225 K.What is the ratio

\frac{Q 3}{Q 1}

Figure Below Represents A Carnot Engine That Works Between T...

Options:

A . 10485

B . 10495

C . 85104

D . 95104

Answer: Option C
:
C
Let us consider the efficiency of the heat engine first.

η_{H . E} = 1 - \frac{T_{2}}{T_{1}}

= 1 - \frac{150}{400} = \frac{5}{8}

∴ W = η_{H . E} \times Q_{1}

= \frac{5}{8} Q_{1}

.......................(1)
Now this work is utilized by the refrigerator to add heat to the hot body from the cold body. The efficiency of this refrigerator is calculated using.

η_{r} = 1 - \frac{T_{3}}{T_{4}}

= 1 - \frac{225}{325}

= \frac{4}{13}

...........(2)
We know that

η_{r} = \frac{Q_{2}}{w}

\Rightarrow Q_{2} = w \times η_{r}

............(3)
From

1^{s t}

law of thermodynamics we know

Q_{3} = Q_{2} + w

= w + w \times η_{r}

- - - - - - (4)
Substituting for w and

e t a_{r}

in (4) we get

Q_{3} = \frac{5}{8} Q_{1} + \frac{5}{8} Q_{1} \times \frac{4}{13}

= Q_{1} (\frac{65 + 20}{8 \times 13})

= Q_{1} \times \frac{85}{104}

\frac{Q_{3}}{Q_{1}} = \frac{85}{104}

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. Figure below represents a Carnot engine that works between temperatures T1 400 K and T2 150 K and drives aCarnot refrige....325 K and T4 225 K.What is the ratio Q3Q1?

Question 2. A window air conditioner is brought into the center of a dorm room and turned on. After several minutes, the temperature....turned on. After several minutes, the temperature of the room:

Question 3. A heat engine executes one complete cycle. The change in entropy of the engine (just the engine, not the external therma....engine (just the engine, not the external thermal reservoirs) is:

Question 4. In one complete cycle, a heat engine extracts heat Qh from a thermal reservoir, does work W and does not eject any heat ....environment. This heat engine is impossible because its operation violates:

Question 5. A typical dorm room or bedroom contains about 2500 moles of air. Find the change in the internal energy of this much air....atm. Treat the air as an ideal gas with γ = 1.400.

Question 6. A vessel contains a mixture of 1 mole of oxygen and two moles of nitrogen at 300 K. The ratio of the rotation....energy per O2 molecule to that per N2 molecule is

Question 7. The graph below represents the Otto-cycle, based on which petrol engines are run.The Otto-cycle engine in a Mercedes-Ben....the ideal efficiency of the engine? Use γ = 1.40.

Question 8. A bubble of 5.00 mol of helium is submerged at a certain depth in liquid water when the water (and thus the helium) unde....during the temperature increase? Use the first law of thermodynamics.

Question 9. 10 moles of oxygen (O2) gas is being expanded in a container, maintained at a constant pressure, by supplying 500J ....the bond axis, and the gas is pretty much ideal

Question 10. An experimenter adds 970 J of heat to 1.75 mol of an ideal gas to heat it from 10.0∘C to 25.0∘C ....internal energy of the gas. (ii) Calculate γ for the gas.

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers