# 13.3 The ideal gas law  (Page 6/11)

 Page 6 / 11

## Section summary

• The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
• The ideal gas law can be written in terms of the number of molecules of gas:
$\text{PV}=\text{NkT},$
where $P$ is pressure, $V$ is volume, $T$ is temperature, $N$ is number of molecules, and $k$ is the Boltzmann constant
$k=1\text{.}\text{38}×{\text{10}}^{–\text{23}}\phantom{\rule{0.25em}{0ex}}\text{J/K}.$
• A mole is the number of atoms in a 12-g sample of carbon-12.
• The number of molecules in a mole is called Avogadro’s number ${N}_{\text{A}}$ ,
${N}_{\text{A}}=6\text{.}\text{02}×{\text{10}}^{\text{23}}\phantom{\rule{0.25em}{0ex}}{\text{mol}}^{-1}.$
• A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
• The ideal gas law can also be written and solved in terms of the number of moles of gas:
$\text{PV}=\text{nRT},$
where $n$ is number of moles and $R$ is the universal gas constant,
$R=8\text{.}\text{31}\phantom{\rule{0.25em}{0ex}}\text{J/mol}\cdot \text{K}.$
• The ideal gas law is generally valid at temperatures well above the boiling temperature.

## Conceptual questions

Find out the human population of Earth. Is there a mole of people inhabiting Earth? If the average mass of a person is 60 kg, calculate the mass of a mole of people. How does the mass of a mole of people compare with the mass of Earth?

Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

## Problems&Exercises

The gauge pressure in your car tires is $2\text{.}\text{50}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ at a temperature of $\text{35}\text{.}0\text{º}\text{C}$ when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to $–\text{40}\text{.}0\text{º}\text{C}$ ?

1.62 atm

Convert an absolute pressure of $7\text{.}\text{00}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ to gauge pressure in ${\text{lb/in}}^{2}\text{.}$ (This value was stated to be just less than $\text{90}\text{.}{\text{0 lb/in}}^{2}$ in [link] . Is it?)

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of $\text{20}\text{.}0\text{º}\text{C}$ . (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is $\text{60}\text{.}0\text{º}\text{C}$ (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final pressure be, taking this into account? Is this a negligible difference?

(a) 0.136 atm

(b) 0.135 atm. The difference between this value and the value from part (a) is negligible.

Large helium-filled balloons are used to lift scientific equipment to high altitudes. (a) What is the pressure inside such a balloon if it starts out at sea level with a temperature of $\text{10}\text{.}0\text{º}\text{C}$ and rises to an altitude where its volume is twenty times the original volume and its temperature is $–\text{50}\text{.}0\text{º}\text{C}$ ? (b) What is the gauge pressure? (Assume atmospheric pressure is constant.)

Confirm that the units of $\text{nRT}$ are those of energy for each value of $R$ : (a) $8\text{.}\text{31}\phantom{\rule{0.25em}{0ex}}\text{J/mol}\cdot \text{K}$ , (b) $1\text{.}\text{99 cal/mol}\cdot \text{K}$ , and (c) $0\text{.}\text{0821 L}\cdot \text{atm/mol}\cdot \text{K}$ .

(a) $\text{nRT}=\left(\text{mol}\right)\left(\text{J/mol}\cdot \text{K}\right)\left(\text{K}\right)=\text{J}$

(b) $\text{nRT}=\left(\text{mol}\right)\left(\text{cal/mol}\cdot \text{K}\right)\left(\text{K}\right)=\text{cal}$

(c) $\begin{array}{lll}\text{nRT}& =& \left(\text{mol}\right)\left(\text{L}\cdot \text{atm/mol}\cdot \text{K}\right)\left(\text{K}\right)\\ & =& \text{L}\cdot \text{atm}=\left({\text{m}}^{3}\right)\left({\text{N/m}}^{2}\right)\\ & =& \text{N}\cdot \text{m}=\text{J}\end{array}$

why no diagrams
where
Fayyaz
Myanmar
Pyae
Describe an experiment to determine short half life
what is science
A 20MH coil has a resistance of 50 ohms and us connected in series with a capacitor to a 520MV supply
what is physics
it is the science which we used in our daily life
Sujitha
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Junior
it is branch of science which deals with study of happening in the human life
AMIT
it is when you get up of your arse and do some real work 😁
A 20MH coil has a resistance of 50 ohms and is connected in series with a capacitor to a 250MV supply if the circuit is to resonate at 100KHZ, Determine 1: the capacitance of the capacitor 2: the working voltage of the circuit, given that pie =3.142
Musa
Physics is the branch of science that deals with the study of matter and the interactions it undergoes with energy
Kelly
Heat is transfered by thermal contact but if it is transfered by conduction or radiation, is it possible to reach in thermal equilibrium?
Yes, It is possible by conduction if Surface is Adiabatic
Astronomy
Yeah true ilwith d help of Adiabatic
Kelly
what are the fundamentals qualities
what is physic3
Kalilu
what is physic
Kalilu
Physics? Is a branch of science dealing with matter in relation to energy.
Moses
Physic... Is a purging medicine, which stimulates evacuation of the bowels.
Moses
are you asking for qualities or quantities?
Noman
give examples of three dimensional frame of reference
your fat arse sitting all day is a good reference of three dimensional numbnut
Universe
Noman
Yes the Universe itself
Astronomy
Examine different types of shoes, including sports shoes and thongs. In terms of physics, why are the bottom surfaces designed as they are? What differences will dry and wet conditions make for these surfaces?
sports shoes are designed in such a way they are gripped well with your feet and their bases have and high friction surfaces, Thong shoes are for comfort, these are easily removed and light weight. these are usually low friction surfaces but in wet conditions they offer greater friction.
Noman
thong sleepers are usually used in restrooms.
Noman
what is wave
The phenomenon of transfer of energy
Noman
how does time flow in one dimension
you mean in three dimensions......numbnut
yeah that was a mistake
Lord
if it flows in three dimensions does it mean if an object theoretically moves beyond the speed of light it won't experience time
Lord
time seems to flow in one direction...but I the past present and future happen every moment time flies regardless.
but if an object moves beyond the speed of light time stops right for it
Lord
yes but at light speed it ceases
Lord
yes it always flow from past to future.
Noman
if v=ktx Ly Mz find the value of x,y and z
x=v=ktx Ly Mz find the value of x,y and z
y=v=ktx Ly Mz find the value of x,y and z
z=v=ktx Ly Mz find the value of x,y and z
now get your lazy arse up and clean the kitchen 😁
I want to join the conversation
😂
hmm
Stephen
what conversation you talking about? .....numbnut
how do i calculate for period of the oscillation
T=2π√(m÷k).K is spring constance
Ambe
T=2π√m/k
Lord
does the force in a system result in the energy transfer?