Question Details

An engine operates on the reversible cycle as shown in the figure. The work output from the engine (in kJ/cycle) is ______ (correct to two decimal places).

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Correct Answer :

62.5

Solution :

The correct answer is 62.5.

For any thermodynamic cycle represented on a pressure-volume (p-V) diagram, the net work output per cycle is equal to the area enclosed by the path of the cycle.

By analyzing the provided p-V diagram, we can observe that the cycle forms a right-angled triangle. The coordinates and limits visible in the image are:
- Pressure (p) is plotted on the vertical axis in kilopascals (kPa), with values ranging from 400 kPa to 650 kPa.
- Volume (V) is plotted on the horizontal axis in cubic meters (m3), with values ranging from 2 m3 to 2.5 m3.

We can determine the base and height of the triangular region representing the cycle:
- Base (ΔV) = 2.5 m3-2 m3=0.5 m3
- Height (Δp) = 650 kPa-400 kPa=250 kPa

The work output is calculated using the formula for the area of a triangle:
Work output=12×Base×Height

Substituting the values into the formula:
Work output=12×0.5 m3×250 kPa

Since the product of pressure in kPa and volume in m3 gives energy in kilojoules (kJ):
Work output=0.25×250=62.5 kJ/cycle

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