In a polytropic process, the relation between pressure and volume is given by $PV^n = \text{constant}$. For an adiabatic process involving an ideal gas, the value of 'n' is equal to:

## CORE INFORMATION\n✓ **Answer**: [C]\n## CONCEPT FRAMEWORK\n\t**Primary Concept**: Polytropic and Adiabatic Processes\n\t**Related Topics**: Thermodynamics, Ideal Gas Law\n\t**Prerequisites**: Understanding of thermodynamic processes, definition of adiabatic process\n## SOLUTION PATHWAY\n**Given Information**:\n\t* Polytropic process: $PV^n = \text{constant}$\n\t* Adiabatic process involving ideal gas\n**Method & Steps**:\n\t1. Identify the specific relationship for an adiabatic process:\n\t\tReasoning: An adiabatic process is defined as a process where no heat is exchanged with the surroundings.\n\t\tFormula/Rule: The relationship for an adiabatic process involving an ideal gas is given by $PV^\gamma = \text{constant}$, where $\gamma$ is the adiabatic index.\n\t2. Compare the given polytropic equation with the adiabatic equation:\n\t\tReasoning: Both equations have the form $PV^n = \text{constant}$, so we can directly compare the exponent n with $\gamma$.\n\t\tWorking: In the adiabatic process, $n = \gamma$.\n\t3. Conclusion:\n\t\tResult: The value of 'n' for an adiabatic process is equal to $\gamma$.\n\t\tVerification: This is a standard result in thermodynamics.\n ## OPTION ANALYSIS\n[A] :x: The value of n=1 corresponds to an isothermal process not an adiabatic one\n[B] :x: The value of n=0 does not represent any standard process\n[C] ✓: For an adiabatic process, the value of n is equal to the adiabatic index, $\gamma$\n[D] :x: The value of $1/\gamma$ is not applicable for an adiabatic process.\n ## LEARNING AIDS\n\t**Common Mistakes**:\n\t\t1.[Error 1]: Confusing adiabatic with isothermal process. [How to avoid]: Remember that adiabatic means no heat exchange, while isothermal means constant temperature.\n\t\t2.[Error 2]: Incorrectly applying the ideal gas law in the adiabatic conditions. [How to avoid]: Understand that the ideal gas law is modified by the adiabatic condition.\n\t**Quick Tips**:\n\t\t1.[Helpful shortcut]: Remember the adiabatic process relation $PV^\gamma = \text{constant}$ and directly relate it to the polytropic equation.\n\t\t2.[Memory aid]: 'Adiabatic' starts with 'a' and the adiabatic index is $\gamma$, which is also a letter.

The correct Option is "$\gamma$"

NEET Questions

Ace NEET 2025 with 70K+ NCERT-based MCQs, PYQs & solutions from expert faculty. Join 150,000+ aspirants on NEET.Guide. Get topic-wise, difficulty-rated practice for Class 11 & 12

Select Subject

In an isothermal process, 200 J of heat is added to a system. What is the change in internal energy of the system?

0 J

200 J

-200 J

400 J

Question Tags

📚 Subject:Physics

📑 Chapter:Thermodynamics

🎯Topic:Different Thermodynamic Process

🎓 Ncert Level:Application

🎯Difficulty :Medium

⚡ Time Required :1 mins

🔄Ncert Concepts :Thermodynamics, Isothermal Process, Internal Energy

32.

A gas undergoes a cyclic process. Which of the following quantities MUST be zero for the entire cycle?

Work done

Heat absorbed

Change in internal energy

Change in temperature

Question Tags

📚 Subject:Physics

📑 Chapter:Thermodynamics

🎯Topic:Different Thermodynamic Process

🎓 Ncert Level:Understanding

🎯Difficulty :Medium

⚡ Time Required :1 mins

🔄Ncert Concepts :Thermodynamics, Cyclic Process, Internal Energy, State Function

33.

Which thermodynamic process occurs at constant pressure?

Isothermal

Adiabatic

Isochoric

Isobaric

Question Tags

📚 Subject:Physics

📑 Chapter:Thermodynamics

🎯Topic:Different Thermodynamic Process

🎓 Ncert Level:Remembering

🎯Difficulty :Medium

⚡ Time Required :1 mins

🔄Ncert Concepts :Thermodynamics, Isobaric Process

34.

In a polytropic process, the relation between pressure and volume is given by $PV^n = ext{constant}$ . For an adiabatic process involving an ideal gas, the value of 'n' is equal to: