When a gas filled in a closed vessel is heated by raising the temperature by $1^{\circ}\mathrm{C}$, its pressure increase by $0.4\%$. The initial temperature of the gas is $\_\_\_\_$ K.

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

When a gas filled in a closed vessel is heated by raising the temperature by

1^{\circ} C

, its pressure increase by

0.4%

. The initial temperature of the gas is

____

Answer: 250

Solution

For an ideal gas at constant volume, from

p V = n R T

, we have:

\frac{Δ p}{p} = \frac{Δ T}{T}

Given that

Δ p / p = 0.4% = 0.004

and

Δ T = 1 K

\frac{0.4}{100} = \frac{1}{T}

T = \frac{100}{0.4} = 250 K

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Integer answer

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 →