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Peter_parker

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- Homework Statement
- Uncertain how to take into account the temperature of the hot cylinder?

- Relevant Equations
- U=m*cv*dt

p*V=m*Rs*T

Task:

A thermally insulated pressurized air cylinder, B, was initially placed inside a closed-bottom, circular hollow cylinder A with an inner diameter of 50 cm. Then a tightly fitting, frictionless sliding piston with a mass of 20 kg was installed. Using the outlet valve, the height of the piston was set to h1 = 100 cm. The pressurized air cylinder B contains 10 liters of hot air with a temperature of 150 °C (TB) and an absolute pressure of 20 bar. The air in container A, that is, outside the pressurized air cylinder B, initially has the ambient temperature.

For your calculations, consider air as an ideal gas with a specific heat capacity at constant volume, cV = 0.718 kJ/(kg·K), and specific gas constant, Rs = 0.287 kJ/(kg·K).

The intrinsic volume of the bottle material should be neglected. The following environmental condition exists: ambient pressure pamb = 1 bar, ambient temperature Tamb = 20 °C.

Question of the homework:

After opening the pressurized air cylinder B, the entire system quickly reaches an equilibrium state. The process is adiabatic. At what height is the piston now located? What temperature does the system reach?

What i did:

Equation1 / Part1:

Condition 1: U1=m_a*cv*T1+m_a*cv*TB= m_both*cv*(T1+TB)

Condition 2: U2=m_both*cv*(T2)

Connection via:U12=Q+Wv with Q =0 and Wv=p*(V1-V2) to m_both*cv*(T2-(T1+TB))=p*(V1-V2)

Equation2 / Part2:

p(V2+VB)=m_both*Rs*T2

By combining Equation 1 and Equation 2, I get T2 / V2 --> then used the area of the cylinder to calculate h2.

However, I'm getting a very unrealistic value for h2. I'm wondering if I made a mistake in the way I included TB in Condition 1. Can anyone spot an mistake in my approach?

Thanks!

A thermally insulated pressurized air cylinder, B, was initially placed inside a closed-bottom, circular hollow cylinder A with an inner diameter of 50 cm. Then a tightly fitting, frictionless sliding piston with a mass of 20 kg was installed. Using the outlet valve, the height of the piston was set to h1 = 100 cm. The pressurized air cylinder B contains 10 liters of hot air with a temperature of 150 °C (TB) and an absolute pressure of 20 bar. The air in container A, that is, outside the pressurized air cylinder B, initially has the ambient temperature.

For your calculations, consider air as an ideal gas with a specific heat capacity at constant volume, cV = 0.718 kJ/(kg·K), and specific gas constant, Rs = 0.287 kJ/(kg·K).

The intrinsic volume of the bottle material should be neglected. The following environmental condition exists: ambient pressure pamb = 1 bar, ambient temperature Tamb = 20 °C.

Question of the homework:

After opening the pressurized air cylinder B, the entire system quickly reaches an equilibrium state. The process is adiabatic. At what height is the piston now located? What temperature does the system reach?

What i did:

Equation1 / Part1:

Condition 1: U1=m_a*cv*T1+m_a*cv*TB= m_both*cv*(T1+TB)

Condition 2: U2=m_both*cv*(T2)

Connection via:U12=Q+Wv with Q =0 and Wv=p*(V1-V2) to m_both*cv*(T2-(T1+TB))=p*(V1-V2)

Equation2 / Part2:

p(V2+VB)=m_both*Rs*T2

By combining Equation 1 and Equation 2, I get T2 / V2 --> then used the area of the cylinder to calculate h2.

However, I'm getting a very unrealistic value for h2. I'm wondering if I made a mistake in the way I included TB in Condition 1. Can anyone spot an mistake in my approach?

Thanks!