The volume of 1 kg of helium in a piston–cylinder device is initially 5 m3. Now helium is compressed to 3 m3 while its pressure is maintained constant at 123 kPa. Determine the work required to compress Helium, in kJ. The gas constant of helium is R = 2.0769 kJ/kg·K. If you got a negative answer please also write the negative sign with your answer.IMPORTANT INSTRUCTION: Put your answer in the text box up to two decimal places or as a whole number.
Question
The volume of 1 kg of helium in a piston–cylinder device is initially 5 m3. Now helium is compressed to 3 m3 while its pressure is maintained constant at 123 kPa. Determine the work required to compress Helium, in kJ. The gas constant of helium is R = 2.0769 kJ/kg·K. If you got a negative answer please also write the negative sign with your answer.IMPORTANT INSTRUCTION: Put your answer in the text box up to two decimal places or as a whole number.
Solution
The work done on a system is given by the equation W = PΔV, where P is the pressure and ΔV is the change in volume.
Given: Initial volume (V1) = 5 m^3 Final volume (V2) = 3 m^3 Pressure (P) = 123 kPa = 123 kJ/m^3 (since 1 kPa = 1 kJ/m^3)
We can calculate the change in volume (ΔV) as V2 - V1 = 3 m^3 - 5 m^3 = -2 m^3.
Substituting the values into the equation, we get:
W = PΔV = 123 kJ/m^3 * -2 m^3 = -246 kJ.
So, the work required to compress the helium is -246 kJ. The negative sign indicates that work is done on the system (compression).
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