Work done by a Carnot engine operating between temperatures $127^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$ is 2 kJ. The amount of heat transferred to the engine by the reservoir is:

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Heat & Thermodynamics

Work done by a Carnot engine operating between temperatures

12 7^{\circ} C

and

2 7^{\circ} C

is 2 kJ. The amount of heat transferred to the engine by the reservoir is:

(A)4 kJ
(B)2 kJ
(C)8 kJ✓ Correct
(D)2.67 kJ

Answer: (C)

Solution

The efficiency of a Carnot engine is

η = 1 - \frac{T _{2}}{T _{1}} = \frac{W}{Q _{1}}

, where

T_{1} = 12 7^{\circ}

C = 400 K and

T_{2} = 2 7^{\circ}

C = 300 K. Thus

η = 1 - \frac{300}{400} = \frac{1}{4}

. Given work done

W = 2

kJ, we have

\frac{2}{Q _{1}} = \frac{1}{4}

. Solving gives

Q_{1} = 8

kJ.

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Heat & Thermodynamics →

More JEE Main questions on Heat & Thermodynamics

A cylindrical tube $A B$ of length $l$ , closed at both ends contains an ideal gas of 1 mol having molecular weight $M$ . The tube is rotated in a horizontal plane with constant angular velocity $ω$ about an axis perpendicular to $A B$ and passing through the edge at end A, as s …
JEE Main 2026View solution →
Rods $x$ and $y$ of equal dimensions but of different materials are joined as shown in figure. Temperatures of end points $A$ and $F$ are maintained at $10 0^{\circ} C$ and $4 0^{\circ} C$ respectively. Given the thermal conductivity of rod x is three …
JEE Main 2026View solution →
The volume of an ideal gas increases 8 times and temperature becomes $(1/4)^{th}$ of initial temperature during a reversible change. If there is no exchange of heat in this process ( $Δ Q = 0$ ) then identify the gas from the following options (Assuming …
JEE Main 2026View solution →
Consider two boxes containing ideal gases A and B such that their temperatures, pressures and number densities are same. The molecular size of A is half of that of B and mass of molecule A is four times that of B. If the collision frequency in gas B is …
JEE Main 2026View solution →
An insulated cylinder of volume $60 cm^{3}$ is filled with a gas at $2 7^{\circ} C$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 cm^{3}$ while allowing the temperature to rise to $7 7^{\circ} C$ . The fin …
JEE Main 2026View solution →
The r.m.s speed of oxygen molecules at $4 7^{\circ} C$ is equal to that of the hydrogen molecules kept at $____$ $^{\circ} C$ . (Mass of oxygen molecule/mass of hydrogen molecule=32/2)
JEE Main 2026View solution →