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What is the work done by air which enters into an evacuated vessel from the atmosphere when the valve is opened? The atmospheric pressure is 1.013 bar, and 1.5 m³ of air at atmospheric conditions enters the vessel.

A. 100.2 kJ
B. 120.5 kJ
C. 140.65 kJ
D. -151.95 kJ

Answer :

D) 151.95 kJ. The work done by air which enters into an evacuated vessel from the atmosphere when the valve is opened.

Given:

  • Atmospheric pressure [tex](P_{atm})[/tex] = 1.013 bar
  • Volume of air entering [tex](V_{air})[/tex] = 1.5 m³

The work done by the air is given by the formula:

W = P * V

Where:

  • P is the atmospheric pressure
  • V is the volume of the air entering the vessel

First, convert the atmospheric pressure to Pascals (SI unit):

1 bar = 10⁵ Pascals

So, 1.013 bar = 1.013 × 10⁵ Pascals

Now, substitute the values into the work formula:

W = 1.013 × 10⁵ Pa × 1.5 m³

W = 151950 Joules

Convert Joules to kilojoules (kJ):

151950 Joules = 151.95 kJ

Since the work is done by the air on the surroundings, it is typically considered positive. Therefore, the correct answer is: (d) 151.95 kJ

Corrected complete question

What is the work done by air which enters into an evacuated vessel from atmosphere when the valve is opened ? The atmospheric pressure is 1.013 bar and 1.5m³ of air at atmospheric condition enters into the vessel.

(a) 100.2 kJ

(b) 120.5 kJ

(c) 140.65 kJ

(d) 151.95 kJ

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