Calculating Gas Volumes and Pressures 1: How do we calculate gas volume and pressure; 2: How is this applied to real life situations ?

Pressure Decreases, Volume increases…

Why is breathing difficult at great altitudes ?

Scattering Ashes into ….Space !

Submarine Escape Training

Pressure Increases…Volume Decreases:

Gas Pressure and Volume Data

Air Tanks: air needs to be compressed to provide enough for the necessary dive length. The gas bottle needs to be able to store a large volume of gas at atmospheric pressure into a few litres. Containing this gas creates a huge pressure.

Boyle’s Law a Volume inversely proportional to pressure. b c

1: Gas Volume : Pressure relationship-

V1xP1 = V2xP2 or V1P1 = V2x P2 …. 2 x 4 = 1 x ? 3 x 4 = ? X 6

V1P1=V2P2 Relationship Volume 1 (V1) (m3) Pressure 1 (P1) (Pa) Volume 2 (V2) (m3) Pressure 2 (P2) (Pa) 6 3 9 240 46 6826 26 000 86 420 482 6.3 x 108 2.7 x 105 8 x 10 8

V1P1=V2P2 Relationship Volume 1 (V1) (m3) Pressure 1 (P1) (Pa) Volume 2 (V2) (m3) Pressure 2 (P2) (Pa) 6 3 9 2 240 46 6826 1.68 26 000 1602.1 86 420 482 6.3 x 108 2.7 x 105 212,625 8 x 10 8

Applying this relationship: A cylinder of O2 contains 0.3m3 of gas at a pressure of 14 000 000 Pa (1.4 x 107). If all the O2 is released without changing temperature, what will its volume be ? ( Atmospheric Pressure = 100 000 Pa)

Applying this relationship: A cylinder of O2 contains 0.3m3 of gas at a pressure of 14 000 000 Pa (1.4 x 107). If all the O2 is released without changing temperature, what will its volume be ? ( Atmospheric Pressure = 100 000 Pa) V2 = P1V1 / P2 V2 = 0.3 m3 x 14 000 000 Pa / 100 000 Pa V2 = 42 m3

Exam Question: V1P1=V2P2 A bicycle pump compresses 0.000 025 m3 of air at atmospheric pressure to a volume of 0.000 010 m3. What is the pressure of the compressed gas ? (Atmospheric Pressure = 100 000 Pa) P2 =V1xP1 / V2

Exam Question: V1P1=V2P2 A bicycle pump compresses 0.000 025 m3 of air at atmospheric pressure to a volume of 0.000 010 m3. What is the pressure of the compressed gas ? (Atmospheric Pressure = 100 000 Pa Ie, P2 = V1 x P1 / V2 (V1) 0.000025 m3 x (P1)100 000 Pa/ 0.000 010 m3 P2 = 250 000 Pa P2 =V1xP1 / V2

Why doing work on a gas increases its temperature: As gas particles are compressed, the pressure increases. The particles hit each other and the moving cylinder more frequently so this speeds up their movement. Faster moving particles have a higher temperature.

2: Temperature and Gas Pressure:

If the temperature of a gas is increased at constant pressure, the volume increases. A hot air balloon contains 2000 m3 of air at 100 0C (373 K). What volume of air at 5 0C (278 K) is needed to fill the balloon ? Use K for temperature units. V2 = (V1/T1) x T2

Temperature and Volume in Gas (You must convert 0C to 0K before calculation) Temperature 1 (0C) Volume 1 (m3) Temperature 2 (0C) Volume 2 (m3) 1 12 100 4 200 420 2.4 1360 20 0.1 -40 0.4 124

3: Higher: Combining the equations- A 0.1 m3 gas cylinder can stand a pressure of 20 x 107 Pa before breaking. It is filled with gas at 2 x107 Pa at 200C. What temperature can it stand before it explodes ? ( Convert 0C to K ) 2 X 9 --------- = 6 3

3: Higher: Combining the equations- A 0.1 m3 gas cylinder can stand a pressure of 20 x 107 Pa before breaking. It is filled with gas at 2 x107 at 200C. What temperature can it stand before it explodes ? ( Convert 0C to K ) Ie, P2 = (P1) 2 x 107 x (V1) 0.1 m3 / (T1) 293 K = 6825.9 (P2) 20 x 107 x (V2) )0.1 m3 / 6825.9 = 2930 K (2657 0C)

Try this…… A gas bottle, volume 0.15 m3, is normally stored at 200C at a pressure of 2.3 x 108 Pa. What is the pressure in the bottle if the temperature rises to 400C ?

Try this…… A gas bottle, volume 0.15 m3, is normally stored at 200C at a pressure of 2.3 x 108 Pa. What is the pressure in the bottle if the temperature rises to 400C ? Ie, what is P2 ? (P1) 2.3 x 108 Pa x (V1) 0.15 m3 / 293 K = 117747.44 P2 = (T2 x 117747.44) / V2 P2 = (313 K x 117747.44) / 0.15m3 = P2 = 245 699 660 Pa or 2.45 x 108 Pa 2 x 9 ------- = 6 3

Higher Level Progression Question (A) A gas bottle, volume 0.15 m3, is normally stored at 210C at a pressure of 2.3 x 108 Pa. What is the pressure in the bottle if the temperature rises to 720C ?

Extension Questions (H+F) 3 Extension Questions (H+F) 1: Patients with lung problems often need to be given extra O2 to breathe. A gas cylinder has a volume of 0.2 m3. It stores O2 at a pressure of 15 000 000 Pa. What would the volume of O2 be if it were released at atmospheric pressure (= 100 000 Pa) ? 2: 1000 m3 of air is used to fill a hot air balloon. The air starts at 100C (283K) and is heated to 700C (343K). What is the volume of air inside the balloon ?