Find out the work done in the following process.

Question

The cycloalkene (X) on bromination consumes one mole of bromine per mole of (X) and gives the product (Y) in which C : Br ratio is \(3:1\). The percentage of bromine in the product (Y) is _________ % (Nearest integer).
Given:
\[ \text{H} = 1,\quad \text{C} = 12,\quad \text{O} = 16,\quad \text{Br} = 80 \]

Answer 1

The problem requires finding the work done during the cyclic process shown in the PV diagram below.

The work done in a cyclic process is equal to the area enclosed by the path on the PV diagram.

Let's calculate the area:

The shape formed seems to be roughly elliptical, simplifying the area calculation.
The formula for the area of an ellipse is A = \pi \cdot a \cdot b, where a is the semi-major axis, and b is the semi-minor axis.
From the diagram, the pressure axis (P) runs from approximately 60 kPa to 340 kPa, giving a total length of 280 \, \text{kPa} and a semi-major axis a = 140 \, \text{kPa}.
The volume axis (V) runs from 60 cm³ to 320 cm³, giving a total length of 260 \, \text{cm}^3 and a semi-minor axis b = 130 \, \text{cm}^3.
Substitute these values into the ellipse area formula:

A = \pi \cdot 140 \, \text{kPa} \cdot 130 \, \text{cm}^3

Since 1 kPa = 1000 Pa and 1 cm³ = 10^-6 m³, the unit conversion gives:

A = \pi \cdot 140 \times 10^3 \, \text{Pa} \cdot 130 \times 10^{-6} \, \text{m}^3

Simplifying:

A = \pi \cdot 140 \cdot 130 \times 10^{-3} \, \text{J}

Calculating the numerical value:

A \approx \pi \times 140 \times 130 \times 10^{-3} \approx 61.5 \, \text{J}

Therefore, the work done is 61.5 Joule.

The correct answer is 61.5 Joule, which matches the given correct option.

Answer 2