Each side of a box made of metal sheet in cubic shape is '$a$' at room temperature '$T$', the coefficient of linear expansion of the metal sheet is '$\alpha$'. The metal sheet is heated uniformly, by a small temperature $\Delta \mathrm{T}$, so that its new temperature is $\mathrm{T}+\Delta \mathrm{T}$. Calculate the increase in the volume of the metal box.

(A) $\frac{4}{3} \pi a^{3} \alpha \Delta T$

(C) $4 \pi a^{3} \alpha \Delta T$

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Heat & Thermodynamics

Each side of a box made of metal sheet in cubic shape is '

a

' at room temperature '

T

', the coefficient of linear expansion of the metal sheet is '

α

'. The metal sheet is heated uniformly, by a small temperature

Δ T

, so that its new temperature is

T + Δ T

. Calculate the increase in the volume of the metal box.

(A) $\frac{4}{3} π a^{3} α Δ T$
(B) $3 a^{3} α Δ T$ ✓ Correct
(C) $4 π a^{3} α Δ T$
(D) $4 a^{3} α Δ T$

Answer: (B)

Solution

The coefficient of volume expansion is

γ = 3 α

.

The initial volume is

V = a^{3}

.

The change in volume is:

Δ V = γ V Δ T = 3 α \cdot a^{3} \cdot Δ T

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · 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 →