Question:
A Carnot engine has an efficiency of \(\frac{1}{6}\). When the temperature of the sink is reduced by \(62^\circ\mathrm{C}\), its efficiency is doubled. The temperatures of the source and the sink are, respectively
A Carnot engine has an efficiency of \(\frac{1}{6}\). When the temperature of the sink is reduced by \(62^\circ\mathrm{C}\), its efficiency is doubled. The temperatures of the source and the sink are, respectively
Show Hint
Use \(\eta = 1 - T_2/T_1\) in kelvin for both situations and solve the two equations.
Updated On: Nov 11, 2026
- \(99^\circ\mathrm{C},\ 37^\circ\mathrm{C}\)
- \(124^\circ\mathrm{C},\ 62^\circ\mathrm{C}\)
- \(37^\circ\mathrm{C},\ 99^\circ\mathrm{C}\)
- \(62^\circ\mathrm{C},\ 124^\circ\mathrm{C}\)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
\(\eta = 1-\frac{T_2}{T_1} = \frac{1}{6}\Rightarrow T_2 = \frac{5}{6}T_1\).
After lowering the sink by 62 K: \(1-\frac{T_2-62}{T_1} = \frac{1}{3}\Rightarrow T_2 - 62 = \frac{2}{3}T_1\).
Subtract: \(\frac{5}{6}T_1 - \frac{2}{3}T_1 = 62\Rightarrow \frac{T_1}{6} = 62\Rightarrow T_1 = 372\ \mathrm{K} = 99^\circ\mathrm{C}\).
\(T_2 = \frac{5}{6}\times 372 = 310\ \mathrm{K} = 37^\circ\mathrm{C}\).
Answer: (1) \(99^\circ\mathrm{C},\ 37^\circ\mathrm{C}\)
After lowering the sink by 62 K: \(1-\frac{T_2-62}{T_1} = \frac{1}{3}\Rightarrow T_2 - 62 = \frac{2}{3}T_1\).
Subtract: \(\frac{5}{6}T_1 - \frac{2}{3}T_1 = 62\Rightarrow \frac{T_1}{6} = 62\Rightarrow T_1 = 372\ \mathrm{K} = 99^\circ\mathrm{C}\).
\(T_2 = \frac{5}{6}\times 372 = 310\ \mathrm{K} = 37^\circ\mathrm{C}\).
Answer: (1) \(99^\circ\mathrm{C},\ 37^\circ\mathrm{C}\)
Was this answer helpful?
0
0
Top JEE Main Physics Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
- $I _{ CM }$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc $I_{A B}$ is it's moment of inertia about an axis $AB$ perpendicular to plane and parallel to axis $CM$ at a distance $\frac{2}{3} R$ from center Where $R$ is the radius of the dise The ratio of $I _{ AB }$ and $I _{ CM }$ is $x: 9$ The value of $x$ is______
- A nucleus disintegrates into two smaller parts, which have their velocities in the ratio $3: 2$ The ratio of their nuclear sizes will be $\left(\frac{x}{3}\right)^{\frac{1}{3}}$ The value of ' $x$ ' is:-
- A particle starts with an initial velocity of 10.0 m/s along x-direction and accelerates uniformly at the rate of 2.0 m/s$^2$. The time taken by the particle to reach the velocity of 60.0 m/s is
View More Questions
Top JEE Main Thermodynamics Questions
- An electric appliance supplies 6000 J/min heat to the system. If the system delivers a power of 90 W. How long it would take to increase the internal energy by $2.5 \times 10^3$ J ?
- The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have:
- Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason (R): In an isothermal process, \( PV = \text{constant} \), while in an adiabatic process \( PV^\gamma = \text{constant} \). Here, \( \gamma \) is the ratio of specific heats, \( P \) is the pressure and \( V \) is the volume of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below: - A poly-atomic molecule (C\(_3\)R, \(C_v = 4R\), where \(R\) is gas constant) goes from phase space point A (\(P_A = 10^4 \, \text{Pa}, V_A = 4 \times 10^{-3} \, \text{m}^3\)) to point B (\(P_B = 5 \times 10^4 \, \text{Pa}, V_B = 6 \times 10^{-7} \, \text{m}^3\)) to point C (\(P_C = 10^4 \, \text{Pa}, V_C = 8 \times 10^{-3} \, \text{m}^3\)). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is:
- Water falls from a height of 200 m into a pool. Calculate the rise in temperature of the water assuming no heat dissipation from the water in the pool. (Take $ g = 10 \, \text{m/s}^2 $, specific heat of water = 4200 J/(kg K))
View More Questions
Top JEE Main Questions
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,
View More Questions