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Physics Question 100 – AP-EAMCET 2026

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If the temperature of 3 moles of helium gas is increased by 2K, then the change in the internal energy of helium gas is

The internal energy of an ideal gas depends only on its temperature. For a monatomic ideal gas, the change in internal energy is directly proportional to the change in temperature and the number of moles.

Step 1: Identify Gas Type and Given Parameters✦ Active

The problem states we have 3 moles of helium gas. Helium is a monatomic ideal gas. The temperature is increased by 2 K. We need to find the change in its internal energy.

💡 Teacher's Secret Hint

Recognizing that helium is a monatomic gas is crucial, as it determines the value of its molar specific heat at constant volume.

Step 2: Determine Molar Specific Heat at Constant Volume (Cv)○ Expand

For a monatomic ideal gas, the molar specific heat at constant volume (Cv) is given by:

Cv=32R

Where R is the ideal gas constant, which is approximately 8.314 J mol−1 K−1. Substituting the value of R:

Cv=32×8.314 J mol−1 K−1=1.5×8.314 J mol−1 K−1=12.471 J mol−1 K−1
💡 Teacher's Secret Hint

Ensure you use the correct value for the ideal gas constant R and the specific formula for Cv for a monatomic gas. For diatomic gases, Cv=52R.

Step 3: Calculate the Change in Internal Energy (ΔU)○ Expand

The change in internal energy (ΔU) for an ideal gas is given by the formula:

ΔU=nCvΔT

We are given n=3 moles, we found Cv=12.471 J mol−1 K−1, and ΔT=2 K. Substitute these values into the formula:

ΔU=(3 mol)×(12.471 J mol−1 K−1)×(2 K)
ΔU=74.826 J

Rounding to one decimal place, the change in internal energy is 74.8 J.

💡 Teacher's Secret Hint

Always check your units. Moles cancel with mol−1, and K cancels with K−1, leaving Joules, which is the correct unit for energy.

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