The ideal gas law PV = nRT gives a relationshipbetween the pressure P in pascals (you can readabout the pressure unit pascals here if you'd like 2),the volume V in cubic meters, n is the number ofmoles of a substance present and R is Avogadro'snumber (you can read about moles and Avogadro'snumber here if you'd like 2 ) and T is the temperaturein Kelvins (here's some information about the Kelvinscale) 2.It's worth mentioning that the ideal gas law assumeswe can ignore things like the volume of individualmolecules and the attraction between particles. So ifwe say something like "Pretend we have an ideal gasin a box," we are quite literally pretending, becausethere is no ideal gas! But this equation is a statementabout the relationship of units to each other, and thusis useful for comparing quantities in an approximateway. In practice, chemists might measure thedeviation from the ideal gas law in order to deduceinformation about other properties.The tools we developed in this unit for comparingrelated rates can help us analyze situations involvingthe ideal gas equation. • Pretend we have some amount of an ideal gas in abox with volume that does not change, and weheat it at a rate of 5 Kelvins per minute.o Which quantities in the ideal gas law representconstants in this situation, and which arevariables?o Which of the derivatives, in the equation yougot using implicit differentiation, do you haveinformation about? Make substitutions asappropriate.o There should be one derivative remaining inthe equation. Isolate it algebraically anddescribe what information you can get fromyour new equation.o Come up with a story problem about what theother quantities in the equation are (make upyour own numbers), and solve your problem.

Volume, number of moles, universal gas constant, Avogadro number are constant quantities.…

• Pretend we have some amount of an ideal gas in a box with volume that does not change, and we heat it at a rate of 5 Kelvins per minute. o Which quantities in the ideal gas law represent constants in this situation, and which are variables? o Which of the derivatives, in the equation you got using implicit differentiation, do you have information about? Make substitutions as appropriate. o There should be one derivative remaining in the equation. Isolate it algebraically and describe what information you can get from your new equation. o Come up with a story problem about what the other quantities in the equation are (make up your own numbers), and solve your problem.

• Pretend we have some amount of an ideal gas in a box with volume that does not change, and we heat it at a rate of 5 Kelvins per minute. o Which quantities in the ideal gas law represent constants in this situation, and which are variables? o Which of the derivatives, in the equation you got using implicit differentiation, do you have information about? Make substitutions as appropriate. o There should be one derivative remaining in the equation. Isolate it algebraically and describe what information you can get from your new equation. o Come up with a story problem about what the other quantities in the equation are (make up your own numbers), and solve your problem.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter2: The Kinetic Theory Of Gases

Section: Chapter Questions

Problem 81AP: One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of...

See similar textbooks

Similar questions

Using a numerical integration method such as Simpson's rule, find the fraction of molecules in a sample of oxygen gas at a temperature of 250 K that have speeds between 100 m/s and 150 m/s. The molar mass of oxygen (O2) is 32.0 g/mol. A precision to two significant digits is enough.
Assuming the human body is primarily made of water, estimate the number of molecules in it. (Note that water has a molecular mass of 18 g/mol and there are roughly 1024 atoms in a mole)
Charles’ law states that for a fixed mass of gas under constant pressure, the volume V and temperature T of the gas (in kelvins) satisfy the equation V = kT, where k is constant. Find an equation relating dV>dt to dT>dt.
The gas law for an ideal gas at absolute temperature T(in kelvins), pressure P (in atmospheres), and volume V(in liters) is PV=nRT, where is the number of moles ofthe gas R =0.0821 and is the gas constant. Suppose that,at a certain instant P=8.0, atm and is increasing at a rateof 0.10 atm/min and V=10L and is decreasing at a rateof 0.15 L/min. Find the rate of change of T with respect totime at that instant if n=10 mol.
What is the volume of 10 mol of gas at the temperature 14°C when the pressure is 138 kPa? Answer in the unit of m3. Be careful with units. Use R = 8.314 J/(K mol) for the gas constant
When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^1.4=C where C is a constant. Suppose that at a certain instant the volume is 440 cubic centimeters and the pressure is 99 kPa and is decreasing at a rate of 7 kPa/minute. 1). At what rate in cubic centimeters per minute is the volume increasing at this instant? (Pa stands for Pascal-- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 100 Pascals)
How many molecules are in a typical object, such as gas in a tire or water in a drink? We can use the ideal gas law to give us an idea of how large N typically is.Calculate the number of molecules in a cubic meter of gas at standard temperature and pressure (STP), which is defined to be 0ºC and atmospheric pressure.
a chemist is doing some measurements with a thermometer that is accurate to 1 degree k and a pressure gauge that is accurate to 2 bars. Using the equation for the ideal gas law, V=C T/P, where C is a constant and V is volume, T is temperature in Kelvin and P is pressure in bars, how far off on volume(Leave C in the problem and ignore it) can he be assuming max error on each measurement assuming he measure 13 bars and 340 degrees K?
How strongly does a linear temperature vs volume graph support the assumption that the volume of a gas under constant pressure is directly proportional to the absolute temperature of the gas?
When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^1.4=C where C is a constant. Suppose that at a certain instant the volume is 450 cubic centimeters and the pressure is 93 kPa and is decreasing at a rate of 14 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? Answer in cm^3/min(Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals. )
Hi, could I get some help with this macro-connection physics problem involving the Ideal Gas Law? The set up is: What is the average volume in nm3 (cubic nanometers) taken up by molecules of an ideal gas at room temperature (taken as 300 K), and 1 atm of pressure or 101325 N/m2 to 4 digits of precision if kB = 1.38e-23 J/K and 1 nm = 10-9 m? Thank you.
The gas law for a fixed mass mm of an ideal gas at absolute temperature T, pressure P, and volume V is PV=mRT, where R is the gas constant. Find the partial derivative (∂P/∂V) (∂V/∂T) (∂T/∂P) = ?