Internal Energy of a Monoatomic Ideal Gas

The total internal energy of two mole monoatomic ideal gas at temperature T=300 K will be J. (Given R=8.31 J / mol. K)

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Question type: Numerical
Exam relevance: JEE Main · Physics
Academic status: Answer verified against the official NTA key
Source: Previous-year question
Editorial review: 22 September 2026

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Students also ask

Why do we use

C_{v}

instead of

C_{p}

when calculating internal energy even if the pressure might be constant?

For an ideal gas, internal energy depends solely on temperature: $d U = n C_{v} d T$ is always true for any process, not just constant volume processes.

Answer

Accepted answer: 7479 J

The total internal energy of two moles of a monoatomic ideal gas at $300 K$ is $7479 J$ .

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Step-by-step solution

Given: Number of moles $n = 2$ , monoatomic gas (degrees of freedom $f = 3$ ), temperature $T = 300 K$ , and universal gas constant $R = 8.31 J / (mol \cdot K)$ .
Find: Total internal energy $U$ of the gas in Joules.
Visualise: A container holds 2 moles of a monoatomic gas at 300 K. The atoms only have 3 translational degrees of freedom, so each molecule contributes $\frac{3}{2} k_{B} T$ on average, or $\frac{3}{2} R T$ per mole.
Strategise: Use the internal energy relation for an ideal gas: $U = n C_{v} T = n (\frac{f}{2} R) T$ . For a monoatomic gas, $f = 3$ , giving $C_{v} = \frac{3}{2} R$ .
Execute: $U = 2 \times (\frac{3}{2} \times 8.31) \times 300 = 3 \times 8.31 \times 300 = 900 \times 8.31 = 7479 J$ .
Verify: Units: $(mol) \times (J / (mol \cdot K)) \times K = J$ . Order of magnitude: $900 \times 8.3 \approx 7470 J$ , which is physically consistent.

Internal Energy of a Monoatomic Ideal Gas

What feels right?

The total internal energy of two moles of a monoatomic ideal gas at $300 K$ is $7479 J$ .

Why each option works or fails

Solution

01Given

02Find

03Visualise

04Strategise

05Execute

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Internal Energy of a Monoatomic Ideal Gas

The total internal energy of two moles of a monoatomic ideal gas at 300 K300 K is 7479 J7479 J.

01Given

02Find

03Visualise

04Strategise

05Execute

✓Verify

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In the estimation of bromine, $0.5 g$ of an organic compound gave…