What is Molar Specific Heat of Diatomic Gas? | Simple Explanation for Class 12

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What is Molar Specific Heat of a Diatomic Gas?

Grade Level:

Class 12

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Definition

What is it?

Molar specific heat of a diatomic gas is the amount of heat energy required to raise the temperature of one mole of that gas by one degree Celsius (or Kelvin). It tells us how much heat a specific amount (one mole) of a diatomic gas can 'hold' for a given temperature change. This value is different when the gas is kept at constant volume (Cv) versus constant pressure (Cp).

Simple Example

Quick Example

Imagine you are making two cups of chai, both with one mole of 'chai gas'. If you heat one cup while keeping its volume fixed (like in a sealed pressure cooker) and the other cup while allowing it to expand (like in an open pan), you'll notice you need to add different amounts of heat to raise their temperature by the same amount. The 'molar specific heat' tells you exactly how much heat is needed for each scenario.

Worked Example

Step-by-Step

Let's find the molar specific heat at constant volume (Cv) for a diatomic gas like Oxygen.

Step 1: For a diatomic gas, the degrees of freedom (f) are 5 (3 translational + 2 rotational).
---Step 2: The molar specific heat at constant volume (Cv) is given by the formula: Cv = (f/2) * R, where R is the universal gas constant (approximately 8.314 J/mol·K).
---Step 3: Substitute the value of f into the formula: Cv = (5/2) * R.
---Step 4: Calculate Cv: Cv = (5/2) * 8.314 J/mol·K.
---Step 5: Cv = 2.5 * 8.314 J/mol·K.
---Step 6: Cv = 20.785 J/mol·K.

Answer: The molar specific heat at constant volume for a diatomic gas like Oxygen is approximately 20.785 J/mol·K.

Why It Matters

Understanding molar specific heat is crucial for designing efficient engines in EVs and rockets in Space Technology. Engineers use this concept to predict how gases behave under different temperatures and pressures, which is vital for creating safe and powerful machines. This knowledge can lead to careers in automotive engineering, aerospace, and even climate science, where gas behavior in the atmosphere is studied.

Common Mistakes

MISTAKE: Using the degrees of freedom for a monatomic or polyatomic gas when calculating for a diatomic gas. | CORRECTION: Always remember that a diatomic gas has 5 degrees of freedom (3 translational + 2 rotational) for calculating Cv and Cp.

MISTAKE: Confusing molar specific heat at constant volume (Cv) with molar specific heat at constant pressure (Cp). | CORRECTION: Cv is heat added at constant volume, while Cp is heat added at constant pressure. Cp is always greater than Cv (Cp = Cv + R).

MISTAKE: Forgetting the units or using incorrect units for R (Universal Gas Constant). | CORRECTION: The units for R are J/mol·K. Ensure your final answer also has the correct units (J/mol·K).

Practice Questions

Try It Yourself

QUESTION: What is the molar specific heat at constant pressure (Cp) for a diatomic gas? (Use R = 8.314 J/mol·K) | ANSWER: Cp = (7/2)R = 3.5 * 8.314 = 29.1 J/mol·K

QUESTION: If 2 moles of a diatomic gas are heated at constant volume, and its temperature increases by 10 K, how much heat energy is supplied? (Use R = 8.314 J/mol·K) | ANSWER: Heat Q = n * Cv * deltaT. Cv = (5/2)R = 20.785 J/mol·K. So, Q = 2 * 20.785 * 10 = 415.7 J.

QUESTION: A diatomic gas is heated from 300 K to 310 K at constant pressure. If the work done by the gas is 16.628 J, how many moles of the gas are present? (Use R = 8.314 J/mol·K) | ANSWER: Work done W = nRΔT. So, 16.628 = n * 8.314 * (310-300). 16.628 = n * 8.314 * 10. n = 16.628 / 83.14 = 0.2 moles.

MCQ

Quick Quiz

For a diatomic gas, what is the ratio of its molar specific heat at constant pressure (Cp) to its molar specific heat at constant volume (Cv)?

1.4

1.66

1.33

1.25

The Correct Answer Is:

For a diatomic gas, Cv = (5/2)R and Cp = (7/2)R. The ratio gamma (γ) = Cp/Cv = (7/2)R / (5/2)R = 7/5 = 1.4. This is a standard value you should remember.

Real World Connection

In the Real World

This concept is vital in understanding how engines work, from your scooter's petrol engine to large industrial turbines. For instance, in an auto-rickshaw engine, the combustion of fuel creates hot gases. Knowing the molar specific heat of these gases helps engineers design the engine to extract maximum work and manage heat efficiently, ensuring your ride is smooth and safe.

Key Vocabulary

Key Terms

Molar: refers to one mole of a substance, which is a specific quantity like a 'dozen' but much larger (6.022 x 10^23 particles). | Diatomic Gas: A gas whose molecules consist of two atoms, like Oxygen (O2) or Nitrogen (N2). | Degrees of Freedom: The number of independent ways a molecule can move or store energy. | Universal Gas Constant (R): A fundamental constant relating energy, temperature, and moles of gas. | Constant Volume (Cv): Heat added when the gas volume doesn't change. | Constant Pressure (Cp): Heat added when the gas pressure doesn't change.

What's Next

What to Learn Next

Now that you understand molar specific heat, you're ready to explore the First Law of Thermodynamics and Adiabatic Processes. These concepts build directly on specific heat, helping you understand how energy transforms in real-world systems like refrigerators and power plants. Keep up the great work!