Thermodynamics perfect gas law

In summary, the question is about the temperature at which a sealed tin can with air inside will burst after being heated to a pressure of 500 kPa. The ideal gas law and its variation, P1/T1=P2/T2, can be used to solve for the temperature, with a result of 459.5 degrees. However, the correct answer is 483 degrees, likely due to a different state equation or the expansion of the can.
  • #1
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Homework Statement



Air inside a sealed tin can is initially at a pressure of 200 kPa and temperature of 20 ◦C. The tin can is
known to burst at a pressure of 500 kPa. If the pressure is raised through heating, at what temperature will
it burst?
If you used an air compressor to pump up the can to high pressure, would the temperature before bursting
be the same? If not, why not?

Homework Equations


Pv=RT
P1/T1=P2/T2



The Attempt at a Solution



I'm confused. Why can't I just use the perfect gas law with constant volume to solve for the second temperature?

I get a result of 459.5degrees but solutions state that the answer should be 483 degrees.
 
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  • #2
I aslo get 459.5C.
Were you dealing with a state equation different than the ideal gas law, like van der Waals?
Or maybe the can is supposed to expand.
 

Related to Thermodynamics perfect gas law

1. What is the perfect gas law and how is it related to thermodynamics?

The perfect gas law, also known as the Ideal Gas Law, is a fundamental equation in thermodynamics that describes the behavior of an ideal gas. It relates the pressure, volume, temperature, and number of moles of a gas in a closed system through the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

2. What are the assumptions made in the perfect gas law?

The perfect gas law assumes that the gas molecules are infinitely small, have no intermolecular forces, and are in constant, random motion. It also assumes that the collisions between the gas molecules and the container walls are perfectly elastic, meaning there is no loss of energy during collisions.

3. How does temperature affect the behavior of a gas according to the perfect gas law?

According to the perfect gas law, as the temperature of a gas increases, its pressure and volume will also increase, assuming the number of moles and the gas constant remain constant. This is because at higher temperatures, the gas molecules have more kinetic energy and move faster, resulting in more frequent and forceful collisions with the container walls, leading to an increase in pressure and volume.

4. Can the perfect gas law be applied to real gases?

The perfect gas law is an idealized equation that assumes certain conditions that are not present in real gases, such as non-zero molecular size and intermolecular forces. Therefore, it may not accurately describe the behavior of real gases. However, it can be a good approximation for real gases at low pressures and high temperatures.

5. How is the perfect gas law related to other thermodynamic laws?

The perfect gas law is related to other thermodynamic laws, such as Boyle's law, Charles's law, and Gay-Lussac's law, which describe the behavior of gases under specific conditions. These laws, along with the perfect gas law, are all based on the fundamental principles of thermodynamics, such as the conservation of energy and the ideal gas assumption.

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