Question:
A Carnot engine has efficiency of $50 \%$ .If the temperature of sink is reduced by $40^{\circ} C$, its efficiency increases by $30 \%$ .The temperature of the source will be :
A Carnot engine has efficiency of $50 \%$ .If the temperature of sink is reduced by $40^{\circ} C$, its efficiency increases by $30 \%$ .The temperature of the source will be :
Updated On: Jul 17, 2025
- $166.7 \,K$
- $255.1 \,K$
- $266.7\, K$
- $367.7 \,K$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct answer is (C) : \(266.7\, K\)
Efficiency , \(η=1-\frac{T_L}{T_H}\)
Given : η = 50%
\(\therefore\frac{1}{2}=1-\frac{T_L}{T_H}\)
when η increases by 30% then,
\(\frac{1}{2}(1.3)=1-(\frac{T_L-40}{T_H})\)
\(⇒\frac{1}{2}(1.3)=\frac{1}{2}+\frac{40}{T_H}\)
\(\therefore T_H=266.7\ K\)
Was this answer helpful?
0
2
Top Questions on carnot cycle
- A Carnot engine operates between temperatures of $ 600 \, \text{K} $ and $ 300 \, \text{K} $. If it absorbs $ 900 \, \text{J} $ of heat from the source, how much work does it perform?
- BITSAT - 2025
- Physics
- carnot cycle
- A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. Calculate the efficiency of the engine.
- AP PGECET - 2024
- Nano Technology
- carnot cycle
- Identify the equation typically used to describe the efficiency of a cyclic process.
- AP PGECET - 2024
- Nano Technology
- carnot cycle
- The P-V diagram of a Carnot's engine is shown in the graph below. The engine uses 1 mole of an ideal gas as working substance. From the graph, the area enclosed by the P-V diagram is
[ The heat supplied to the gas is 8000 J ]
- KCET - 2023
- Physics
- carnot cycle
- In a Carnot’s engine, as the gas gives heat energy to the sink, then the temperature of the sink
- AP EAPCET - 2023
- Physics
- carnot cycle
View More Questions
Questions Asked in JEE Main exam
- If the equation of the parabola with vertex $\left(\frac{3}{2},\, 3\right)$ and the directrix $x + 2y = 0$ is
$$ ax^2 + by^2 - cxy - 30x - 60y + 225 = 0, $$ then $\alpha + \beta + \gamma$ is equal to:- JEE Main - 2025
- Calculus
- In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $ t_1 $ and $ t_2 $ (s), respectively. The ratio $ t_1 / t_2 $ will be:
- JEE Main - 2025
- Chemical Kinetics
- HA $ (aq) \rightleftharpoons H^+ (aq) + A^- (aq) $ The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 °C. The dissociation constant for the acid is Given: $ K_f(H_2O) = 1.8 \, \text{K kg mol}^{-1} $, molality ≡ molarity
- JEE Main - 2025
- Colligative Properties
20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _____ M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O = 16 g mol$^{-1}$)
- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
- Which of the following binary mixture does not show the behavior of minimum boiling azeotropes?
- JEE Main - 2025
- Solutions
View More Questions
Concepts Used:
Carnot Cycle
Carnot's Theorem:
From the second law of thermodynamics, two important results are derived where the conclusions are taken together to constitute Carnot’s theorem. It may be stated in the following forms.
- ‘No engine can be more efficient than a perfectly reversible engine working between the same two temperatures’.
- ‘The efficiency of all reversible engines, working between the same two temperatures is the same, whatever the working substances’.
Carnot’s Ideal Heat Engine
- A cylinder having perfectly non-conducting walls, a perfectly conducting base and is provided with a perfectly non-conducting piston which moves without friction in the cylinder. The cylinder contains one mole of perfect gas as the working substance.
- Source: A reservoir maintained at a constant temperature T1 from which the engine can draw heat by perfect conduction. It has an infinite thermal capacity and any amount of heat can be drawn from it at constant temperature T1.
- Heat insulating stand. A perfectly mom-conducting platform acts as a stand for adiabatic processes.
- Sink: A reservoir maintained at a constant lower temperature T2 (T2 < T1) to which the heat engine can reject any amount of heat. The thermal capacity of sink is infinite so that its temperature remains constant at T2, no matter how much heat is given to it.