Combine equation 2 and 3  
푻
푻
푷푽  
푻
P ∝  
→
P = k  
……… make k the subject Then;  
=
Constant  
푽
푽
푷ퟏ퐕ퟏ  
퐓ퟏ  
푷ퟐ퐕ퟐ  
퐓ퟐ  
∴
=
Standard Temperature and Pressure (STP)  
•
•
STP is a set of conditions for experimental measurements to enable comparisons between  
sets of data.  
The standard temperature is 0 °C (273 K) while the standard pressure is 1 atmosphere  
(1.013 x 105 Pa or 760 mm of mercury).  
Worked examples  
1. 125 cm³ of gas are collected at 15 °C and 755 mm of mercury pressure. Calculate the  
volume of this gas at s.t.p. (standard temperature and pressure).  
ANS: given; P1 = 755 mmHg, V1 = 125 cm³, T1 = (273+15) =288 K.  
P2 = 760 mmHg, T2 = (273 + 0) = 273 K, V2 = ?  
푃 푉  
2
2
푃푉  
푃1푉1  
Since  
= Constant, it follows that  
=
푇
푇
푇
2
1
푃 푉 푇  
1
125×755×273 = 117.7 cm3  
1
2
=
=
푉2  
760×288  
푃 푇  
2
1
Therefore, the volume of gas at s.t.p  
≈
118 cm3  
0
2. A bicycle pump contains 50 cm3 of air at 17 C and at 1.0 atmosphere pressure. Find the  
pressure when the air is compressed to 10 cm3 and its temperature rises to 27 0C.  
푃 푉  
2
2
푃푉  
푃1푉1  
From;  
= Constant, it follows that  
=
푇
푇
푇
2
1
푃 푉 푇  
1×50×300 = 5.17  
1
1
2
=
=
푃
Class Activity – 6:8  
1. A sample of oxygen gas has a volume of 0.11 m3 at a temperature of 12 °C and a pressure of  
8.1 x 105 Pa while a sample of nitrogen gas has a volume of 0.18 m3 at a temperature of 22 °C  
and a pressure of 1.03 x 105 Pa. Which gas will have the larger volume at STP?  
(
ANS: V2O = 0.084 m3 , V2N = 0.17 m3 At STP, nitrogen gas would have a volume that  
is more than twice the volume of oxygen gas.)  
2. A fixed mass of gas has a volume of 1.25 litres at a pressure of 76.0 cm of mercury and a  
temperature of 27.0°C. The gas expands to a volume of 1.55 litres raising the pressure to 80.0  
cm of mercury. What is the final temperature of the gas in °C? (ANS: T2 = 391.58K = 118.58°)  
3.  
A fixed mass of gas occupies a volume of 0.001 m3 at a pressure of 76 cmHg. What volume  
does the gas occupy at 17.0°C if its pressure is 72 cmHg? (A: V2 =1.12 x 10-3 m3)  
4.  
It is found that on heating a gas its volume increases by 50% and its pressure decreases to  
60% of its original value. If the original temperature was -15°C, find the temperature to which it  
was heated. [ANS; T2 = -40.80C or 232.2K]  
5. 2500 cm3 of hydrogen is taken at STP. The pressure of this gas is further increased by two and  
a half times (temperature remaining constant). What volume will hydrogen occupy now?  
[ANS; V2 = 714.29 cm3]  
0
6. 50 cm3 of hydrogen is collected over water at 17 C and 750 mmHg pressure. Calculate the  
volume of a dry gas at STP. The water vapour pressure at 17 0C is 14 mmHg.  
ANS; Presssure of dry hydrogen  
,
푃ퟏ = ퟕퟓퟎ − ퟏퟒ = ퟕퟑퟔ풎풎푯품, 푷ퟐ = ퟕퟔퟎ풎풎푯품  
푽ퟏ = ퟓퟎ풄풎ퟑ, 푻ퟏ = ퟏퟕ + ퟐퟕퟑ = ퟐퟗퟎ푲, 푻ퟐ = ퟐퟕퟑ푲 → V2 = 45.58cm3  
100 cm3 of gas A was collected at 10°C and 78.0 cmHg pressure, while 120 cm3 of gas B was  
collected at 50°C and 70.0 cmHg pressure. Which of the two gases is denser at STP? ANS:  
At STP, gas B has large volume than gas A so gas A is denser than gas B . That is VA2 =  
99.00 cm3 and VB2 = 93.42 cm3  
7.  
8. 250 cm3 of a gas are collected at 25°C and 750 mm of mercury. Calculate the volume of the  
gas at STP (ANS: V2 =226.01 cm3)  
9. A sample of carbon dioxide occupies 30 cm3 at 15°C and 740 mm pressure. Find its volume at  
STP. [ANS; 27.7cm3  
]
10. At 0°C and 760 mmHg pressure, a gas occupies a volume of 100 cm3. Kelvin temperature of  
the gas is increased by one-fifth and the pressure is increased one and a half times. Calculate  
the final volume of the gas [ANS; V = 80 cm3]  
Self Assessment – 6  
1. Define coefficient of linear expansion. A copper pipe which is 1 meter long at 150 C increases  
in length by 0.15% when carrying steam at 1000 c, find the coefficient of linear expansion of  
copper  
2. Explain why a compound metal bar made up of two strips, one of iron and another of  
brass, bends when heated  
3. A beaker containing water is heated a temperature of 230 C to 900 C. State and explain what  
happens to the Mass, volume and density of water  
4. An aluminium lid on an ordinary glass jar fits so tightly that it cannot be unscrewed .Should the  
jar and lid be immersed in hot or cold cold water to loosen the lid?. Explain your answer  
5. A steel tower has a height of 324 m at a temperature of 180 C .How tall is the tower on a day  
when the temperature is 350 C?  
6. A brass road of length of 0.997 m at 200 C is hung from a steel framework with a height of 1.00  
m at 200 C as shown in the figure below.  
At what temperature would the brass rod just touch the floor?  
7. A brass has a hole whose radius is too small for an iron rivet to fit in .Explain two ways the rivet  
can be made to fit in the hole  
8. Convert the following temperatures on the Celsius scale to temperatures on the Kelvin  
or absolute scale (a) 1000 C (b) 250 C  
(c ) -1000 C  
9. Convert the following temperatures on the Kelvin scale to temperatures on Celsius scale:  
(a) 273K  
(b) 400K  
(c) 100K  
10. State Charles law and describe how it is verified in laboratory.1000 cm3 of air at 0°C are  
heated to 70°C. What volume will the air occupy if the pressure remains at atmospheric  
throughout?  
11. The pressure of 440cm³ of the gas is 80cm of mercury. What will be the new pressure of the  
gas if its volume is reduced to 400cm³ at constant temperature?  
12. The pressure in a metal glass cylinder at 15°c is 2 atmospheres. At what temperature  
will the pressure be doubled?  
13. When is a given mass of a gas said to be at s.t.p? The volume of a gas collected at a  
temperature of 36° C and pressure of 78cm of mercury is 230cm³. Find its volume at s.t.p.  
14. The figure below shows a brass invar bimetallic strip at room temperature  
Given that brass expands more than invar when both are heated equally, sketch the  
appearance of the strip after being cooled to several degrees below room temperature  
15. A glass test tube was heated over a Bunsen burner flame. Cold water was then quickly poured  
into the test tube. Explain why the test tube would break when cold water is poured in.  
16. A rally a car tyre is at an air pressure 3 x 10⁵ Pa and a temperature of 27°C at start of the  
rally. The temperature rises to 57°C when the car is racing. Assuming the tyre does not  
expand, what is the new pressure in the tyre?  
17. The pressure of 3 m³ at a gas at 27°C is 3 atmospheres .What will be the pressure of the gas if  
it is compressed into a half the volume and heated to 102°C?  
18. (a). Define the term linear expansivity of a solid .  
(b).The original length of ametal bar is 101.5cm at 15°C.Determine the linear expansivity of the  
metal if the bar increases in length by 1.41mm when the temperature is raised to 100°C  
19. Why electrical cables are left sagging during installation?  
20. A metal rod 80cm long increased in length by 0.09 cm when the temperature was raised by  
93.6°C .Determine linear expansivity of metal.  
21. The air in a bicycle tyre occupies a volume of 1000 cm³ when it is at a pressure of 2.5  
atmospheres the air is released to the atmospheres  
(i) Assuming that the temperature of the gas does not change, what volume does it occupy at  
the atmosphere  
(ii) A pump with a volume of 150 cm³ per stroke is used to inflate the tyre .What is the  
pressure of the tyre after two strokes?  
22. An iron rod is 100 cm long at 0°C. What must be the length of alluminium rod at 0°C if the  
difference between the length of the two rods are to remain the same at all temperatures?  
(Linear expansivities of iron and alluminium are 1.2 x 10-5 K-1 and 2.4 x 10-5 K-1, respectively)  
23. A gas occupies a volume of 2m ³ when its pressure is 1140mmHg at a temperature of 27°  
C. What volume will it occupy at s.t.p?  
24. The figure below shows a circuit diagram for controlling the temperature of a room  
(a) State and explain the purpose of the bimettalic strip.  
(b).Describe how the circuit controls the temperature when the switch is closed.  
25. A container holds a gas at 0°C .To what temperature must be heated to its pressure to  
double? (Assume that the volume of the container does not change )  
26. Explain why a glass container with thick walls is more likely to crack than one with thin walls  
when a very hot liquid is poured in each of the glasses  
27. A balloon is filled with air to a volume of 200ml At a temperature of 20°C .The balloon is  
then dipped in water at 80°C.Assuming two leakage occurs and ignoring the pressure  
change due to the water. Calcuate the new volume of air.  
28. A compound strip of brass and iron, 10 cm long at 200C,is held horizontally with iron  
uppermost. When heated from below with a Bunsen burner the temperature of the brass is  
8200 C and that of the iron is 7700C.Calculate the difference in lengths of the iron and brass  
(
ANS:∆풍 = ퟎ. ퟎퟔퟐ 풄풎)  
29. State any three applications of bimetallic strip  
30. Using the kinetic theory of gases explain how a rise in the temperature of gases causes a rise  
in the pressure of a gas when a volume is held constant.  
31. The pressure indicated by the gauge on a constant -volume gas thermometer in a  
thermal equilibrium with a room is 97 kPa .When the thermometer was immersed in a  
bath of ice water, the pressure was 90kPa .What is the temperature in the room in °C?.  
32. Helium gas at temperature of -30°C is held in a rigid metal container at a pressure of 1.5 x 10⁵  
pa. The container is heated to a temperature of 25°C.W hat is the new pressure of the gas?  
33. A metal rod is 10 m long at 200 C .At what temperature would its length increases by 5cm if its  
∆푳  
ퟎ.ퟎퟓ  
linear expansivity is 2x 10-6/K [ANS; 푻ퟐ = 푻ퟏ  
= ퟐퟓퟐퟎ0C  
+
= ퟐퟎ +  
−ퟔ  
푳 ∝  
ퟏ
ퟏퟎ×ퟐ×ퟏퟎ  
34. A cylinder closed at both ends as an inner diameter of 0.021 m. The cylinder is fitted with a  
movable piston of mass of 2 kg. The space between the piston and the bottom of the cylinder  
contains 1.11 x 10-⁴ m³ of air at 25°C while the space above the piston has been evacuated as  
shown in the figure below.  
(a) Determine the pressure of the air in the cylinder given that the pressure comes from the  
weight of the cylinder  
(b) The cylinder is placed over a source of heat causing the air to expand and push the piston  
upward a distance of 3.5cm as shown in the figure below  
Assuming that the pressure of the air remained constant, what was the change in volume of  
the air? (Volume of a cylinder =  
휋
r2h)  
35. Distinguish between heat and temperature  
36. (a) State Charles’ Law ,Boyle’s Law and the Pressure Law  
(b) Write down the ideal gas equation  
(c) The volume of a certain gas at 100 C is 100 cm3 .Calculate the volume of the gas if it  
is warmed at a temperature of 300 C at constant pressure  
37. Explain each of the following observations:  
(a) A lid on a metal can be unscrewed easily if the can is immersed in hot water for a few  
minutes  
(b) Corrugated iron – sheet roofs make cracking noises on a night preceded by a hot day  
(c) It is difficult to unscrew wheel nuts in the morning, while it is relatively easy to unscrew  
them on a hot day.  
38. Define ; (a) Thermal expansion  
(c) Absolute zero temperature (c) Anomalous expansion of water  
39. Differentiate between  
(b) Linear expansivity  
(a) Apparent expansion of liquid and absolute expansion of liquid  
(b) Heat and temperature  
40. What do you understand by intermediate expansion of liquid?  
41. Show how the combined gas law is obtained  
42. Explain the following observations:  
(a) An inflated balloon hung in the open at a wedding bust when the temperature of the  
environment rises  
(b) A whale cannot survive in a shallow water  
(c) Soda bottles are thick  
(d) Water bubbles seem to increase in size as they rise from the bottom of a tank  
(e) Electric wire are seem to sag when its hot but look very straight when its cold  
(f) Fish living in polar regions such as Antarctica do not die even when the  
temperature fall below 0°C  
43. Mention two demerits of anomalous expansion  
44.  
(a) State Boyle’s law.  
(b) Sketch the graph of pressure (P) against the reciprocal of volume (1/v) for air at constant  
temperature  
(c) A bubble of air of volume 50.0mm3 is released by a diver at a depth where the pressure is  
304.0 cm Hg .Assuming that the temperature remains constant ,what is its volume  
before reaches the surface where the pressure is 76.0 cm  
just  
45. A piece of copper is dropped into water, if the temperature of the water is rising what is  
happening to the copper?  
46. Why are the over head power cables more likely to break and fall during the cold season of the  
year than during the warm season of the year even though they carry the same weight all year  
round?  
47. A grandfather’s clock is controlled by a swinging brass pendulum of length 1.3 m at a  
temperature of 20°C.(  
∝
=19 x 10-6 °C-¹)  
(a) What is the length of the pendulum rod when the temperature drops to 0°C?  
풍
(b) If the period of the pendulum is given by T=2  
흅
√
, where L is its length, does the  
품
change in the length or the brass rod cause the clock to run fast or slowly?  
48. A gas is a contained in an 8 litre vessel at a temperature of 20°C and pressure of 9 atm. At  
what temperature will the gas fill 3 litre vessel at a pressure of 13 atmospheres?  
49. The temperature of a body is 47°C .What would this temperature be in the absolute scale?  
50. Given that at s.t.p a gas occupies 5600cm³, determine the pressure at which it will occupy the  
volume of 28.5 litres at a temperature of 220°C.  
51. States Charles’ Law .An ideal occupies a volume of 500 cm3 at a temperature of 300 C .At  
what temperature will it occupy a volume of 456 cm3  
52. Explain why inflated balloon swells up and even bursts when in the open on a hot day?  
53. A form three student carried out an experiment on one of the gas laws .She obtained the  
following results  
Temp T (0C)  
10  
5.0  
35  
5.8  
60  
6.4  
80  
7.0  
90  
7.2  
110  
7.8  
Volume V (cm3)  
(a) Plot a graph of volume V against temperature  
(b) From the graph ,determine the volume of the gas at 00 C  
(c) Determine the slope of the graph  
54. State Boyle’s Law. A gas occupies a volume of 600 cm3 at a pressure of 760 mmHg.  
Determine its volume at a pressure of 1085 mmHg  
55. The volume of a bubble at the base of a container of water is 3 cm3 .The depth of water is 30  
cm. The bubble rises up the column until the surface.  
(a) Explain what happens to the bubbles as it rises up the water column  
(b) Determine the volume of the bubble at a point 12 cm below the water surface  
56. Explain the following  
(a) Deep sea animals cannot survive at regions with shallow waters  
(b) Determine the volume of the bubble at a point 12 cm below the water surface