A monatomic gas having γ = 5/3 is stored in a thermally insulated container and the gas is suddenly compressed to (1/8)ᵗʰ of its initial volume. The ratio of final pressure and initial pressure is:

 

🔥 Adiabatic Compression of Monatomic Gas | Thermodynamics | JEE Physics | Doubtify

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📌 Question:

A monatomic gas having $\gamma = \frac{5}{3}$ is stored in a thermally insulated container, and the gas is suddenly compressed to $\frac{1}{8}^\text{th}$of its initial volume.
What is the ratio of final pressure to initial pressure?

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🖼️ Question Image:

🧠 Solution Image:

🧪 Concept Used:

This is a standard JEE question from adiabatic processes in thermodynamics. Since the gas is in a thermally insulated container, the adiabatic relation applies:

$$P V^{\gamma} = \text{constant}$$

Which leads to:

$$\frac{P_2}{P_1} = \left( \frac{V_1}{V_2} \right)^\gamma$$

Given:

• $\gamma = \frac{5}{3}$

• $\frac{V_2}{V_1} = \frac{1}{8} \Rightarrow \frac{V_1}{V_2} = 8$
  

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🔢 Step-by-Step Solution:

$$\frac{P_2}{P_1} = (8)^{5/3} = 2^5 = \boxed{32}$$

✅ Final Answer:

$$\boxed{\frac{P_2}{P_1} = 32}$$

🎯 Why This Question Is Important:

• It directly tests your understanding of adiabatic compression

• Teaches you how to apply γ (gamma) values properly in real-world physics problems

• Commonly asked in JEE Main & Advanced and even NEET

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🎥 Video Solution:

🧠 Pro Tip:

In any adiabatic process, there is no heat exchange – always use

$$PV^\gamma = \text{constant}$$

and remember:

• Monatomic gas ⇒ $\gamma = \frac{5}{3}$

• Diatomic gas ⇒ $\gamma = \frac{7}{5}$

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