A body cools in 7 minutes from $60^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. The temperature of the surrounding is $10^{\circ} \mathrm{C}$. The temperature of the body after the next 7 minutes will be:

JEE Main · 2023 · 06 Apr 2023 · Shift 2 · Heat & Thermodynamics

A body cools in 7 minutes from

6 0^{\circ} C

4 0^{\circ} C

. The temperature of the surrounding is

1 0^{\circ} C

. The temperature of the body after the next 7 minutes will be:

(A) $3 2^{\circ} C$
(B) $3 0^{\circ} C$
(C) $2 8^{\circ} C$ ✓ Correct
(D) $3 4^{\circ} C$

Answer: (C)

Solution

Newton's law of cooling in the approximate form

\frac{T _{1} - T _{2}}{t} = K (\frac{T _{1} + T _{2}}{2} - T_{s})

applies to each interval. For the first seven minutes

\frac{60 - 40}{7} = K (50 - 10)

, giving

K = \frac{1}{14}

. For the next seven minutes

\frac{40 - T}{7} = \frac{1}{14} (\frac{40 + T}{2} - 10)

, which reduces to

4 (40 - T) = 20 + T

, so

5 T = 140

. The temperature after the next seven minutes is

2 8^{\circ}

JEE Main · 2023 · 06 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 →