Question 705040

SCQMEDIUM

The following $P - V$ diagram shows a process, where an ideal gas is taken quasi-statically from $A$ to $B$ along the path as shown in the figure. The work done $W$ in this process is:

(A)

$\frac{1}{4}(V_2 - V_1)(3P_2 + P_1)$

(B)

$\frac{1}{4}(V_2 - V_1)(3P_2 - P_1)$

(C)

$\frac{1}{2}(V_2 - V_1)(P_1 + P_2)$

(D)

$\frac{1}{2}(V_2 + V_1)(P_2 - P_1)$

Detailed Solution

The work done $W$ is the area under the $P-V$ graph. The area can be divided into three parts: a trapezoid, a rectangle, and a rectangle. Alternatively, splitting the shape under the curve into a rectangle at the bottom and a trapezoid on top:

Area = $\int P dV$ .

The total area under the path from $V_1$ to $V_2$ is calculated by summing the areas of the geometric components defined by the path.

Performing the integration or geometric decomposition leads to $Area = \frac{1}{4}(V_2 - V_1)(3P_2 + P_1)$ .

Question 705040

Detailed Solution

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