Answered

Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Join our platform to connect with experts ready to provide accurate answers to your questions in various fields. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Three kg of gas in a piston–cylinder assembly undergo a process during which the relationship between pressure and specific volume is Pv0.5=constant. The process begins with P1=250 kPa and V1=1.5 m3 and ends with P2=100 kPa. Determine the final specific volume, in m3/kg.

Sagot :

oladayoademosu

The final specific volume in m³/kg is 0.0313 m³/kg.

Since [tex]Pv^{0.5} = constant[/tex] where P = pressure and v = specific volume, we have

Since [tex]P_{1} v_{1}^{0.5} = P_{2} v_{2}^{0.5}[/tex] where

  • P₁ = initial pressure = 250 kPa,
  • v₁ = initial specific volume = V₁/m where
  • V₁ = initial volume of gas = 1.5 m³ and
  • m = mass of gas = 3 kg. so, v₁ = V₁/m = 1.5 m³/3 kg = 0.5 m³/kg,
  • P₂ = final pressure = 100 kPa,
  • v₂ = final specific volume of gas

Final Specific volume

Making v₂ subject of the formula, we have

[tex]v_{2} = v_{1} ( \frac{P_{1} }{P_{2} }) ^{2}[/tex]

Substituting the values of the variables into the equation, we have

[tex]v_{2} = v_{1} ( \frac{P_{1} }{P_{2} }) ^{2}[/tex]

[tex]v_{2} = 0.5 \frac{m^{3} }{kg} ( \frac{250 kPa }{100 kPa }) ^{2}\\v_{2} = 0.5 \frac{m^{3} }{kg} ( \frac{25}{10}) ^{2}\\v_{2} = 0.5 \frac{m^{3} }{kg} ( 0.25) ^{2}\\v_{2} = 0.5 \frac{m^{3} }{kg} (0.0625)\\v_{2} = 0.0313 \frac{m^{3} }{kg}[/tex]

The final specific volume in m³/kg is 0.0313 m³/kg.

Learn more about specific volume of gas here:

https://brainly.com/question/15128372

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.