The total internal energy of two mole monoatomic ideal gas at temperature $\mathrm{T}=300 \mathrm{~K}$ will be \_\_\_\_ J. (Given $\mathrm{R}=8.31 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}$)

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · Heat & Thermodynamics

The total internal energy of two mole monoatomic ideal gas at temperature

T = 300 K

will be ____ J. (Given

R = 8.31 J / mol \cdot K

)

Answer: 7479

Solution

For a monoatomic ideal gas, the internal energy is

U = n C_{v} T

, where

C_{v} = \frac{3}{2} R

. With

n = 2

moles and

T = 300

U = 2 \times \frac{3}{2} \times 8.31 \times 300 = 3 \times 8.31 \times 300 = 7479

JEE Main · 2022 · 28 Jun 2022 · Shift 1 · 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 →