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

#### Questions & Answers

What does mean ohms law imply
what is matter
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
Alo
the time rate of increase in velocity is called
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
how to solve pressure?
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
what is accuracy and precision
How does a current follow?
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH
what is Atom? what is molecules? what is ions?
What is a molecule
Is a unit of a compound that has two or more atoms either of the same or different atoms
Justice
A molecule is the smallest indivisible unit of a compound, Just like the atom is the smallest indivisible unit of an element.
Rachel
what is a molecule?
Vineeta
what is a vector
A quantity that has both a magnitude AND a direction. E.g velocity, acceleration, force are all vector quantities. Hope this helps :)
deage
what is the difference between velocity and relative velocity?
Mackson
Velocity is the rate of change of displacement with time. Relative velocity on the other hand is the velocity observed by an observer with respect to a reference point.
Chuks
what do u understand by Ultraviolet catastrophe?
Rufai
A certain freely falling object, released from rest, requires 1.5seconds to travel the last 30metres before it hits the ground. (a) Find the velocity of the object when it is 30metres above the ground.
Mackson
A vector is a quantity that has both magnitude and direction
Rufus
the velocity Is 20m/s-2
Rufus
derivation of electric potential
V = Er = (kq/r^2)×r V = kq/r Where V: electric potential.
Chuks
what is the difference between simple motion and simple harmonic motion ?
syed
hi
Peace
hi
Rufus
hi
Chip
simple harmonic motion is a motion of tro and fro of simple pendulum and the likes while simple motion is a linear motion on a straight line.
Muinat
a body acceleration uniform from rest a 6m/s -2 for 8sec and decelerate uniformly to rest in the next 5sec,the magnitude of the deceleration is ?
The wording not very clear kindly
Moses
6
Leo
9.6m/s2
Jolly
the magnitude of deceleration =-9.8ms-2. first find the final velocity using the known acceleration and time. next use the calculated velocity to find the size of deceleration.
Mackson
wrong
Peace
-3.4m/s-2
Justice
Hi
Abj
Firstly, calculate final velocity of the body and then the deceleration. The final ans is,-9.6ms-2
Muinat
8x6= 48m/-2 use v=u + at 48÷5=9.6
Lawrence
can i define motion like this motion can be define as the continuous change of an object or position
Any object in motion will come to rest after a time duration. Different objects may cover equal distance in different time duration. Therefore, motion is defined as a change in position depending on time.
Chuks