Question 153: Thermodynamics & KTG

Question

Using the given $P-V$ diagram, the work done by an ideal gas along the path $A B C D$ is :

Accepted Answer

To find the work done by an ideal gas along the path $ABCD$ on the given $P-V$ diagram, we calculate the work done on each segment individually and then sum them up.
Segment $AB$:
The work is given by $	ext{w}_{AB} = P_0 	imes V_0$, contributing $P_0 V_0$.
Segment $BC$:
No volume change occurs along this path, resulting in zero work: $	ext{w}_{BC} = 0$.
Segment $CD$:
The gas compresses, performing negative work: $	ext{w}_{CD} = -(2P_0 	imes 2V_0) = -4P_0 V_0$.
Adding the work done in each segment:
$ \begin{align*} 	ext{w}_{ABCD} &= 	ext{w}_{AB} + 	ext{w}_{BC} + 	ext{w}_{CD} \ &= P_0 V_0 + 0 - 4P_0 V_0 \ &= -3P_0 V_0 \end{align*} $
Thus, the total work done by the gas along the path $ABCD$ is $-3P_0 V_0$.

Answer

$3 \mathrm{P}_0 \mathrm{~V}_0$

Answer

$-3 \mathrm{P}_0 \mathrm{~V}_0$

Answer

$-4 \mathrm{P}_0 \mathrm{~V}_0$

Answer

$4 \mathrm{P}_0 \mathrm{~V}_0$

Thermodynamics & KTG

Using the given P-V diagram, the work done by an ideal gas along the path A B C D is :

Choose the correct answer: