Question 710: Thermodynamics & KTG

Question

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

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: