to one another. Set them equal to each other in an equation.- Solve for the final temperature and evaluate.
Physics principles and equations
The ideal gas law
PV = nRT
The temperature is given in Celsius and will need to be converted to Kelvin to apply the ideal gas law.
Step-by-step solution
We start by using the ideal gas law to write an equation relating the initial and final conditions of the gas.We can solve for the final temperature because all the other values are known. The initial temperature was stated in Celsius, but the ideal gas
law requires that kelvins be used, so we add 273 to the Celsius temperature to convert.This is very hot! When tanks like this are filled, they are usually held under cold water to increase the heat flow out of the tank and reduce their
temperature increase.Step Reason
1. PiVi = nRTi ideal gas law, initial condition
2. divide by temperature
3. ideal gas law, final condition
4. from steps 2 and 3
Step Reason
5. solve for Tf
6. substitute values
7. Tf = 439 K evaluate
8. Tf = (439 – 273) = 166°C convert to Celsius
19.7 - Interactive problem: pressure of an ideal gas
In this simulation, a small chamber contains an ideal gas consisting of 26 gas
particles held at a constant temperature of 400 K. The gas has a pressure of
897 Pa. The chamber volume is currently set at 1.6×10í^22 m^3.
You can change the volume of the chamber, within a range of 0.5×10í^22 m^3 to
2.5×10í^22 m^3. You also can vary the number of gas particles, from 10 to 30. Your
task is to set the number of particles and the volume of gas so that the gas pressure
is reduced to 552 Pa. The temperature of the gas in this simulation remains fixed at
400 K.
When you launch the simulation, you will see the gas particles moving around as
determined by the settings stated above. After running for a few moments, the
simulation will pause so that you can enter your values. Determine how to alter the
volume and the number of molecules to achieve the target pressure of 552 Pa.
Specify these values using the up and down arrows in the control panel and press
GO to apply the new settings to the gas.
A text message will tell you whether the gas reached the correct pressure. You can
also note the pressure in the pressure gauge in the simulation.
If you get the wrong answer, you can try again. Press RESET to return the gas to its initial conditions, specify new values, and press GO again.
If you have trouble with this simulation, review the section on the ideal gas law.(^366) Copyright 2000-2007 Kinetic Books Co. Chapter 19