Calculate net work done by the gas whose thermodynamical behaviour is represented by right angled triangle ABC on `P-V` diagram. The `P-V` diagram co-ordinates are : `A(20, 6), B(10, 12)` and `C(10, 6)` where `P` is in `Nm^(-2)` and `V` is in `m^(3)`

Answer

To calculate the net work done by the gas represented by the right-angled triangle ABC on the P-V diagram, we can follow these steps:

### Step 1: Identify the coordinates of points A, B, and C.
- A(20, 6)
- B(10, 12)
- C(10, 6)

### Step 2: Understand the shape of the triangle.
The triangle ABC is formed by the points A, B, and C in the P-V diagram. The base of the triangle is AC, and the height is BC.

### Step 3: Calculate the lengths of the base and height.
- **Base (AC)**: This is the horizontal distance between points A and C.
- AC = Volume at A - Volume at C = 20 - 10 = 10 m³

- **Height (BC)**: This is the vertical distance between points B and C.
- BC = Pressure at B - Pressure at C = 12 - 6 = 6 Nm²

### Step 4: Calculate the area of triangle ABC.
The area of a triangle is given by the formula:
\[ \text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height} \]
Substituting the values we calculated:
\[ \text{Area} = \frac{1}{2} \times 10 \, \text{m}^3 \times 6 \, \text{Nm}^{-2} = \frac{1}{2} \times 60 = 30 \, \text{Joules} \]

### Step 5: Conclude the net work done by the gas.
The net work done by the gas during the process represented by the triangle ABC is 30 Joules.

### Final Answer:
The net work done by the gas is **30 Joules**.

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