JEE Main · 2020 · 05 Sep 2020 · Shift 2 · Heat & Thermodynamics

WhatsApp Email

In adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be

n

times the initial pressure. The value of

n

is:

(A)128✓ Correct
(B) $\frac{1}{32}$
(C)32
(D)326

Answer: (A)

Solution

In an adiabatic change

P V^{γ}

is constant, and with fixed mass

V \propto \frac{1}{ρ}

, so

P \propto ρ^{γ}

. For a diatomic gas

γ = \frac{7}{5}

. With the density rising to

32

times its initial value,

\frac{P _{f}}{P _{i}} = (32)^{7/5} = (2^{5})^{7/5} = 2^{7} = 128

, so

n = 128

JEE Main · 2020 · 05 Sep 2020 · 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 →