A solid metallic cube having total surface area 24 $\mathrm{m}^{2}$ is uniformly heated. If its temperature is increased by $10^{\circ} \mathrm{C}$, calculate the increase in volume of the cube (Given : $\alpha=5.0 \times 10^{-4}{ }^{\circ} \mathrm{C}^{-1}$ )

(B) $1.2 \times 10^{5} \mathrm{~cm}^{3}$

(A) $2.4 \times 10^{6} \mathrm{~cm}^{3}$

(C) $6.0 \times 10^{4} \mathrm{~cm}^{3}$

(D) $4.8 \times 10^{5} \mathrm{~cm}^{3}$

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Heat & Thermodynamics

A solid metallic cube having total surface area 24

m^{2}

is uniformly heated. If its temperature is increased by

1 0^{\circ} C

, calculate the increase in volume of the cube (Given :

α = 5.0 \times 1 0^{- 4}^{\circ} C^{- 1}

)

(A) $2.4 \times 1 0^{6} cm^{3}$
(B) $1.2 \times 1 0^{5} cm^{3}$ ✓ Correct
(C) $6.0 \times 1 0^{4} cm^{3}$
(D) $4.8 \times 1 0^{5} cm^{3}$

Answer: (B)

Solution

Volume expansion is given by

Δ V = γ V_{0} Δ T

, where

γ = 3 α

. Total surface area

6 a^{2} = 24 m^{2}

gives side

a = 2 m

, so volume

V_{0} = 8 m^{3}

. Then

Δ V = 3 \times 5.0 \times 1 0^{- 4} \times 8 \times 10 = 0.12 m^{3} = 1.2 \times 1 0^{5} cm^{3}

JEE Main · 2022 · 25 Jun 2022 · 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 →