Physics Q98 – AP-EAMCET 2026

Home Physics ThermodynamicsQuestion #498

If the ratio of specific heats of a gas is

1.4

, then the gas is

Clue 1 of 3: Degrees of Freedom

The ratio of specific heats for a gas ( $γ$ ) is directly related to its degrees of freedom ( $f$ ).

🧠 Full Solution Path

Step 1: Recall the Formula for Ratio of Specific Heats✦ Active

The ratio of specific heats, denoted by $γ$ (gamma), for a gas is related to its degrees of freedom ( $f$ ) by the formula:

γ = 1 + \frac{2}{f}

💡 Teacher's Secret Hint

Degrees of freedom refer to the number of independent ways a molecule can move or store energy. For ideal gases, these typically include translational and rotational modes.

Step 2: Determine Degrees of Freedom for Different Gas Types○ Expand

Let's list the degrees of freedom ( $f$ ) for different types of ideal gases at moderate temperatures (where vibrational modes are generally not excited):

1. **Monoatomic gas:** (e.g., He, Ne, Ar) has $f = 3$ (three translational degrees of freedom).

2. **Diatomic gas:** (e.g., O $_{2}$ , N $_{2}$ , H $_{2}$ ) has $f = 5$ (three translational and two rotational degrees of freedom).

3. **Triatomic non-linear gas:** (e.g., H $_{2}$ O) has $f = 6$ (three translational and three rotational degrees of freedom).

4. **Triatomic linear gas:** (e.g., CO $_{2}$ ) also has $f = 5$ at moderate temperatures (three translational and two rotational degrees of freedom), similar to a diatomic gas, as rotation about its axis doesn't store significant energy.

💡 Teacher's Secret Hint

Remember that vibrational degrees of freedom only become active at very high temperatures, leading to an increase in 'f' and a decrease in ' $γ$ '.

Step 3: Calculate

γ

for Each Gas Type and Compare○ Expand

Now, we calculate $γ$ for each type of gas using the formula $γ = 1 + \frac{2}{f}$ :

1. **Monoatomic gas ( $f = 3$ ):**

γ = 1 + \frac{2}{3} = \frac{5}{3} \approx 1.67

2. **Diatomic gas ( $f = 5$ ):**

γ = 1 + \frac{2}{5} = \frac{7}{5} = 1.4

3. **Triatomic non-linear gas ( $f = 6$ ):**

γ = 1 + \frac{2}{6} = 1 + \frac{1}{3} = \frac{4}{3} \approx 1.33

The problem states that the ratio of specific heats is $1.4$ . Comparing this value with our calculations, we find that it matches the value for a diatomic gas.

💡 Teacher's Secret Hint

The value $1.4$ is a key identifier for diatomic gases like air (which is primarily N $_{2}$ and O $_{2}$ ). Memorizing the $γ$ values for common gas types can save time in exams.

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Physics Question 98 – AP-EAMCET 2026

Clue 1 of 3: Degrees of Freedom

🧠 Full Solution Path