Thermodynamic Systems - Volume, Final Pressure and Final Temperature

• Lewishio
In summary, using the ideal gas law and consistent units, we can determine that a mass of 0.12 kg of air with an initial temperature of 500°C and pressure of 0.8 MPa will have an initial volume of 33L. If the air is expanded according to the law pV^1.2 = c to a final volume of 90L, the final pressure will be 240,002.4 Pa and the final temperature will be 627.1K or 354.1°C.
Lewishio
Homework Statement
I have had a go at the following question but have gone wrong somewhere, any ideas?

A mass of 0.12 kg of air has an initial temperature of 500°C and pressure 0.8 MPa. If the air is
expanded according to the law pV1.2 = c to a final volume of 90 litres, determine

i) its initial volume,
ii) its final pressure,
iii) its final temperature.

For air, take R = 287 Jkgˉ¹ Kˉ¹.
Relevant Equations
pV = mRT
V = mRT/P
T = PV/mR
Mass = 0.12kg
Initial temp = 500°c = 773K
Initial pressure = 0.8 MPa = 800,000 Pa
Final volume = 90L
R = 287 Jkg^-1K^-1

1) Initial Volume

V=mRT/P

0.12 x 287 x 773 / 800,000 = 26,662.12m^3

2) Final Pressure

P2 = P1P2^1.2/V2^1.2

800,000 x 26,662.12^1.2 / 90 = 1,816,095,330 Pa = 1,816 MPa

3) Final Temperature

T=P2V2^1.2/mR

1,816,095,330 x 90 / 0.12 x 287 = 1,291 x 10^11 K

Lewishio said:
Problem Statement: I have had a go at the following question but have gone wrong somewhere, any ideas?

A mass of 0.12 kg of air has an initial temperature of 500°C and pressure 0.8 MPa. If the air is
expanded according to the law pV1.2 = c to a final volume of 90 litres, determine

i) its initial volume,
ii) its final pressure,
iii) its final temperature.

For air, take R = 287 Jkgˉ¹ Kˉ¹.
Relevant Equations: pV = mRT
V = mRT/P
T = PV/mR

Mass = 0.12kg
Initial temp = 500°c = 773K
Initial pressure = 0.8 MPa = 800,000 Pa
Final volume = 90L
R = 287 Jkg^-1K^-1

1) Initial Volume

V=mRT/P

0.12 x 287 x 773 / 800,000 = 26,662.12m^3
You forgot to divide by 800000, and you forgot to convert to liters.

Lewishio
Hi,

Thank you, how does this look? I think there is a problem with the formula for the final temperature as my answer is not correct.

1) Initial Volume

V=mRT/P
0.12 x 287 x 773 / 800,000 = 0.033m^3

Convert to litres:
0.033 x 1000 = 33L

2) Final Pressure

P2 = P1V1^1.2 / V2^1.2
800,000 x 33^1.2 / 90^1.2 = 240,002.4 Pa

3) Final Temperature

T = PV^1.2 / mR
240,002.4 x 90^1.2 / 0.12 x 287 = 1.27 x 10^11 K

Lewishio said:
Hi,

Thank you, how does this look? I think there is a problem with the formula for the final temperature as my answer is not correct.

1) Initial Volume

V=mRT/P
0.12 x 287 x 773 / 800,000 = 0.033m^3

Convert to litres:
0.033 x 1000 = 33L

2) Final Pressure

P2 = P1V1^1.2 / V2^1.2
800,000 x 33^1.2 / 90^1.2 = 240,002.4 Pa

3) Final Temperature

T = PV^1.2 / mR
240,002.4 x 90^1.2 / 0.12 x 287 = 1.27 x 10^11 K
The final temperature is incorrect. You should be using the ideal gas law. You should be using consistent units with the volume. And you should learn how to do math using parenthesis for the denominator.

Lewishio
Hi,

I have had another go, how does this look?

PV=mRT rearranged to T= PV/mR

(240,002.4Pa x 0.09m^3) / (0.12kg x 287 Jkg^-1K^-1) = 627.1K = 354.1°c

Chestermiller

1. What is a thermodynamic system?

A thermodynamic system is a physical system that is studied using the principles of thermodynamics, which is the study of energy and its transformations. It can be a closed system, where no mass is exchanged with its surroundings, or an open system, where mass can be exchanged with its surroundings.

2. How is volume related to thermodynamic systems?

Volume is an important property of a thermodynamic system as it determines the amount of space the system occupies. In a closed system, the volume remains constant, while in an open system, the volume can change due to the exchange of mass with its surroundings.

3. What is the final pressure of a thermodynamic system?

The final pressure of a thermodynamic system is the pressure at the end of a process or change in state. It is dependent on factors such as temperature, volume, and the amount of gas present in the system. It can be calculated using the ideal gas law, which states that pressure is inversely proportional to volume and directly proportional to temperature.

4. How is final temperature determined in a thermodynamic system?

The final temperature of a thermodynamic system is the temperature at the end of a process or change in state. It is dependent on factors such as pressure, volume, and the amount of heat added or removed from the system. It can be calculated using the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system.

5. What is the significance of understanding thermodynamic systems?

Understanding thermodynamic systems is crucial in many fields, including chemistry, physics, and engineering. It allows us to predict and control the behavior of physical systems, such as engines and refrigerators, and to understand the fundamental principles behind energy conversion and efficiency. It also helps us to make informed decisions about energy use and sustainability.

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