1. Home
  2. Siyavula textbooks: grade 11
  3. Thermal properties and ideal
  4. Ideal gas law and general gas

5.1 Ideal gas law and general gas equation

<< Chapter < Page
  Siyavula textbooks: grade 11     Page 1 / 4
Chapter >> Page >

The general gas equation

All the gas laws we have described so far rely on the fact that at least one variable (T, p or V) remains constant. Since this is unlikely to be the case most times, it is useful to combine the relationships into one equation. These relationships are as follows:

Boyle's law: p ∝ 1 V (constant T)

Relationship between p and T: p ∝ T (constant V)

If we combine these relationships, we get p ∝ T V

If we introduce the proportionality constant k, we get p = k T V

or, rearranging the equation...

p V = k T

We can also rewrite this relationship as follows:

p V T = k

Provided the mass of the gas stays the same, we can also say that:

p 1 V 1 T 1 = p 2 V 2 T 2

In the above equation, the subscripts 1 and 2 refer to two pressure and volume readings for the same mass of gas under different conditions. This is known as the general gas equation . Temperature is always in kelvin and the units used for pressure and volume must be the same on both sides of the equation.

Remember that the general gas equation only applies if the mass of the gas is fixed.

At the beginning of a journey, a truck tyre has a volume of 30 dm 3 and an internal pressure of 170 kPa. The temperature of the tyre is 16 ∘ C. By the end of the trip, the volume of the tyre has increased to 32 dm 3 and the temperature of the air inside the tyre is 35 ∘ C. What is the tyre pressure at the end of the journey?

  1. p 1 = 170 kPa and p 2 = ?

    V 1 = 30 dm 3 and V 2 = 32 dm 3

    T 1 = 16 ∘ C and T 2 = 40 ∘ C

  2. Here, temperature must be converted into Kelvin, therefore:

    T 1 = 16 + 273 = 289 K

    T 2 = 40 + 273 = 313 K

  3. Use the general gas equation to solve this problem:

    p 1 × V 1 T 1 = p 2 × V 2 T 2

    Therefore,

    p 2 = p 1 × V 1 × T 2 T 1 × V 2
  4. p 2 = 170 × 30 × 313 289 × 32 = 173 k P a

    The pressure of the tyre at the end of the journey is 173 kPa.

Got questions? Get instant answers now!

A cylinder that contains methane gas is kept at a temperature of 15 ∘ C and exerts a pressure of 7 atm. If the temperature of the cylinder increases to 25 ∘ C, what pressure does the gas now exert? (Refer to [link] to see what an 'atm' is.

  1. p 1 = 7 atm and p 2 = ?

    T 1 = 15 ∘ C and T 2 = 25 ∘ C

  2. Here, temperature must be converted into Kelvin, therefore:

    T 1 = 15 + 273 = 288 K

    T 2 = 25 + 273 = 298 K

  3. Since the volume of the cylinder is constant, we can write:

    p 1 T 1 = p 2 T 2

    Therefore,

    p 2 = p 1 × T 2 T 1
  4. p 2 = 7 × 298 288 = 7 . 24 a t m

    The pressure of the gas is 7.24 atm.

Got questions? Get instant answers now!

A gas container can withstand a pressure of 130 kPa before it will start to leak. Assuming that the volume of the gas in the container stays the same, at what temperature will the container start to leak if the gas exerts a pressure of 100 kPa at 15 ∘ C?

  1. p 1 = 100 kPa and p 2 = 130 kPa

    T 1 = 15 ∘ C and T 2 = ?

  2. Here, temperature must be converted into Kelvin, therefore:

    T 1 = 15 + 273 = 288 K

  3. Since the volume of the container is constant, we can write:

    p 1 T 1 = p 2 T 2

    Therefore,

    1 T 2 = p 1 T 1 × p 2

    Therefore,

    T 2 = T 1 × p 2 p 1
  4. T 2 = 288 × 130 100 = 374 . 4 K = 101 . 4 ∘ C
Got questions? Get instant answers now!

Questions & Answers

Discuss the differences between taste and flavor, including how other sensory inputs contribute to our  perception of flavor.
John Reply
taste refers to your understanding of the flavor . while flavor one The other hand is refers to sort of just a blend things.
Faith
While taste primarily relies on our taste buds, flavor involves a complex interplay between taste and aroma
Kamara
which drugs can we use for ulcers
Ummi Reply
omeprazole
Kamara
what
Renee
what is this
Renee
is a drug
Kamara
of anti-ulcer
Kamara
Omeprazole Cimetidine / Tagament For the complicated once ulcer - kit
Patrick
what is the function of lymphatic system
Nency Reply
Not really sure
Eli
to drain extracellular fluid all over the body.
asegid
The lymphatic system plays several crucial roles in the human body, functioning as a key component of the immune system and contributing to the maintenance of fluid balance. Its main functions include: 1. Immune Response: The lymphatic system produces and transports lymphocytes, which are a type of
asegid
to transport fluids fats proteins and lymphocytes to the blood stream as lymph
Adama
what is anatomy
Oyindarmola Reply
Anatomy is the identification and description of the structures of living things
Kamara
what's the difference between anatomy and physiology
Oyerinde Reply
Anatomy is the study of the structure of the body, while physiology is the study of the function of the body. Anatomy looks at the body's organs and systems, while physiology looks at how those organs and systems work together to keep the body functioning.
AI-Robot
what is enzymes all about?
Mohammed Reply
Enzymes are proteins that help speed up chemical reactions in our bodies. Enzymes are essential for digestion, liver function and much more. Too much or too little of a certain enzyme can cause health problems
Kamara
yes
Prince
how does the stomach protect itself from the damaging effects of HCl
Wulku Reply
little girl okay how does the stomach protect itself from the damaging effect of HCL
Wulku
it is because of the enzyme that the stomach produce that help the stomach from the damaging effect of HCL
Kamara
function of digestive system
Ali Reply
function of digestive
Ali
the diagram of the lungs
Adaeze Reply
what is the normal body temperature
Diya Reply
37 degrees selcius
Xolo
37°c
Stephanie
please why 37 degree selcius normal temperature
Mark
36.5
Simon
37°c
Iyogho
the normal temperature is 37°c or 98.6 °Fahrenheit is important for maintaining the homeostasis in the body the body regular this temperature through the process called thermoregulation which involves brain skin muscle and other organ working together to maintain stable internal temperature
Stephanie
37A c
Wulku
what is anaemia
Diya Reply
anaemia is the decrease in RBC count hemoglobin count and PVC count
Eniola
what is the pH of the vagina
Diya Reply
how does Lysin attack pathogens
Diya
acid
Mary
I information on anatomy position and digestive system and there enzyme
Elisha Reply
anatomy of the female external genitalia
Muhammad Reply
Organ Systems Of The Human Body (Continued) Organ Systems Of The Human Body (Continued)
Theophilus Reply
what's lochia albra
Kizito
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply
<< Chapter < Page Page > Chapter >>

Read also:

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Siyavula textbooks: grade 11 physical science. OpenStax CNX. Jul 29, 2011 Download for free at http://cnx.org/content/col11241/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 11 physical science' conversation and receive update notifications?

Ask