Question 710: Thermodynamics & KTG

Question

Which of the following graphs between pressure and volume correctly show isochoric process?
![](https://app-content.cdn.examgoal.net/fly/@width/image/jaoe38c1m4iga4yt/3373260e-7de1-474b-baa3-e50817ce4285/0ccc5d50-b6f4-11ef-b5be-7f8e8357552d/file-jaoe38c1m4iga4yu.png?format=png)

Accepted Answer

To determine the final pressure after the given processes, we can follow these steps:
Isothermal Expansion:
Initial pressure and volume of the gas are $ P $ and $ V $, respectively.
The gas undergoes an isothermal expansion to a volume $ 4V $.
For an isothermal process, the relationship between pressure and volume is given by:
$    P_1 V_1 = P_2 V_2    $
Substituting the given values:
$    P \cdot V = P_2 \cdot 4V    $
Solving for $ P_2 $, we get:
$    P_2 = \frac{P}{4}    $
Adiabatic Compression:
Next, the gas undergoes adiabatic compression back to the original volume $ V $.
For an adiabatic process, the equation is:
$    P_2 V_2^\gamma = P_3 V_3^\gamma    $
Given that $ V_2 = 4V $, $ V_3 = V $, and $\gamma = \frac{3}{2}$:
$    \frac{P}{4} \cdot (4V)^\gamma = P_3 \cdot V^\gamma    $
Substituting $\gamma = \frac{3}{2}$, this becomes:
$    \frac{P}{4} \cdot (4V)^{3/2} = P_3 \cdot V^{3/2}    $
Simplifying further:
$    \frac{P}{4} \cdot 4^{3/2} = P_3    $
Since $4^{3/2} = 8$, we have:
$    P_3 = \frac{P}{4} 	imes 8 = 2P    $
Thus, the final pressure after the entire process is $2P$.

Answer

D

Answer

A

Answer

C

Answer

B

Thermodynamics & KTG

Which of the following graphs between pressure and volume correctly show isochoric process?

Choose the correct answer: