Question

A monoatomic gas undergoes adiabatic change. Its pressure \(P\) and temperature \(T\) are related as \(P\propto T^{x}\) where \(x\) is

• A. \(3.5\)
• B. \(2.5\)
• C. \(4.5\)
• D. \(1.5\)

Hint:

Use the adiabatic relation between P and T, which gives the exponent gamma divided by gamma minus one, with gamma 5/3 for a monoatomic gas.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
For an adiabatic process, \(P^{1-\gamma}T^{\gamma}=\text{constant}\), so \(P\propto T^{\frac{\gamma}{\gamma-1}}\).

Step 2: Value of gamma
For a monoatomic gas, \(\gamma=\frac{5}{3}\).

Step 3: Calculation
\(x=\frac{\gamma}{\gamma-1}=\frac{5/3}{2/3}=2.5\)

Step 4: Compare the options
This is option (B).

Final Answer:
The exponent x equals 2.5. \[ \boxed{\text{(B) }2.5} \]