Find the final temperature? (Ideal Gas Law)

In summary, the conversation is about finding the final temperature in a PV relationship problem, where PV^1.2 = constant. The initial pressure, volume, and temperature are given, as well as the final volume. The conversation includes a link to the attempted solution and a question about the mistake in the final temperature calculation. After receiving help and suggestions, the user realizes their mistake and corrects their calculation. The final temperature is now accurately calculated.
  • #1
elephunk
23
0

Homework Statement



Find the final temperature?

PV relationship -- PV^1.2 = constant

P1 = initial pressure = 720 kN/m^2
V1 = initial volume = 0.4 m^3
V2 = final volume = 1.2 m^3
T1 = initial temperature = 225 C

I managed to get the final pressure part out of the way but don't know where to head with the temperature. Can someone please point me in some direction?

Homework Equations


The Attempt at a Solution



The attempt at a solution and question can be found here: http://i45.photobucket.com/albums/f98/pastilles/Scan10012.jpg

Thanks for your help :)
 
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  • #2
Hi elephunk, welcome to the board. Your work looks good... you did it right but it looks like you made a mistake in the math.
 
  • #3
Hi,

Thanks for the welcome :)

Can you point me to where I am going wrong? Maybe looking at this at nearly 1am in the morning isn't good :(
 
  • #4
Your final pressure looks good, but your final temperature does not. The method seems correct, so it's probably a simple arithmetic error.
 
  • #5
It looks from your attachment that you've calculated the final temperature to be 4 K. Is that what you meant the answer to be?
 
  • #6
Your math seemed okay to me. What about this? Its been a while since Chem I but maybe??

http://img199.imageshack.us/img199/9922/scannedimage038.jpg
 
Last edited by a moderator:
  • #7
Thanks. It was a math error.

Got it sorted now. Thanks all and thinks lizzyb for the the working out :)
 

Related to Find the final temperature? (Ideal Gas Law)

1. What is the Ideal Gas Law and how is it used to find the final temperature?

The Ideal Gas Law is a mathematical equation that relates the properties of an ideal gas (such as pressure, volume, and temperature) to each other. The equation is PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature. To find the final temperature, we rearrange the equation to T = (PV)/(nR) and plug in the known values.

2. What are the units for each variable in the Ideal Gas Law?

The units for pressure (P) are typically in atmospheres (atm) or Pascals (Pa). Volume (V) is usually measured in liters (L) or cubic meters (m^3). The number of moles (n) is dimensionless, meaning it has no units. The ideal gas constant (R) has a value of 0.0821 L·atm/mol·K and its units are determined by the units of pressure, volume, and temperature used in the equation. Temperature (T) is most commonly measured in Kelvin (K), but can also be in Celsius (°C) or Fahrenheit (°F) as long as the units are consistent.

3. Can the Ideal Gas Law be used for any gas or are there limitations?

The Ideal Gas Law is based on certain assumptions about gases, such as that they are in a constant temperature and pressure environment and that the gas particles have no volume. Therefore, it is most accurate for ideal gases, which do not exist in real life. However, it can still be used for real gases as long as they are at low pressures and high temperatures.

4. What are the steps to solving a problem using the Ideal Gas Law to find the final temperature?

The first step is to identify the known variables in the problem, such as pressure, volume, and number of moles. Then, rearrange the Ideal Gas Law equation to solve for temperature. Next, plug in the known values and the ideal gas constant. Finally, solve for the final temperature and make sure to include the correct units.

5. Can the Ideal Gas Law be used for reactions that involve changes in temperature and pressure?

Yes, the Ideal Gas Law can be used for reactions that involve changes in temperature and pressure. However, in these cases, the equation must be modified to account for the changes. This can be done using the combined gas law, which adds a third variable, temperature, to the equation. The combined gas law is (P1V1/T1) = (P2V2/T2), where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.

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