16IB Gas Laws [34 marks]
1.
A thin-walled cylinder of weight W, open at both ends, rests on a flat surface. The cylinder has a height L, an average radius R and a[1 mark]
thickness x where R is much greater than x.
What is the pressure exerted by the cylinder walls on the flat surface?
A.
W
2πRx
B.
W
πR2x
C.
W
πR2
D.
W
πR2L
Markscheme
A
Examiners report
[N/A]
2.
A fixed mass of an ideal gas in a closed container with a movable piston initially occupies a volume V. The position of the piston is [1 mark]
changed, so that the mean kinetic energy of the particles in the gas is doubled and the pressure remains constant.
What is the new volume of the gas?
A.
V
4
B.
V
2
C. 2V
D. 4V
Markscheme
C
Examiners report
[N/A]
3.
A sealed container contains a mixture of oxygen and nitrogen gas.
The ratio
mass of an oxygen molecule
mass of a nitrogen molecule
The ratio
average kinetic energy of oxygen molecules
average kinetic energy of nitrogen molecules
[1 mark]
is 87 .
is
A. 1.
B.
7
.
8
C.
8
.
7
D. dependent on the concentration of each gas.
Markscheme
A
Examiners report
[N/A]
4.
An ideal gas has a volume of 15 ml, a temperature of 20 °C and a pressure of 100 kPa. The volume of the gas is reduced to 5 ml
and the temperature is raised to 40 °C. What is the new pressure of the gas?
[1 mark]
A. 600 kPa
B. 320 kPa
C. 200 kPa
D. 35 kPa
Markscheme
B
Examiners report
[N/A]
5.
An ideal gas of N molecules is maintained at a constant pressure p. The graph shows how the volume V of the gas varies with
absolute temperature T.
What is the gradient of the graph?
A.
N
p
B.
NR
p
C.
Nk B
p
D.
N
Rp
[1 mark]
Markscheme
C
Examiners report
[N/A]
6.
The pressure of a fixed mass of an ideal gas in a container is decreased at constant temperature. For the molecules of the gas there [1 mark]
will be a decrease in
A. the mean square speed.
B. the number striking the container walls every second.
C. the force between them.
D. their diameter.
Markscheme
B
Examiners report
[N/A]
3
7.
0.46 mole of an ideal monatomic gas is trapped in a cylinder. The gas has a volume of 21 m
3
and a pressure of 1.4 Pa.
[5 marks]
(i) State how the internal energy of an ideal gas differs from that of a real gas.
(ii) Determine, in kelvin, the temperature of the gas in the cylinder.
(iii) The kinetic theory of ideal gases is one example of a scientific model. Identify two reasons why scientists find such models useful.
Markscheme
i
«intermolecular» potential energy/PE of an ideal gas is zero/negligible
ii
THIS IS FOR USE WITH AN ENGLISH SCRIPT ONLY
use of T =
PV
nR
or T =
1.4×21
0.46 × 8.31
Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.
Award [2] for a bald correct answer in K.
Award [2 max] if correct 7.7 K seen followed by –265°C and mark BOD. However, if only –265°C seen, award [1 max].
7.7K
Do not penalise use of “°K”
ii
THIS IS FOR USE WITH A SPANISH SCRIPT ONLY
T=
PV
nR
Award mark for correct re-arrangement as shown here not for quotation of Data Booklet version.
T=
1.4×2.1× 10−6
0.46 × 8.31
Uses correct unit conversion for volume
T = 7.7×10-6K
Award [2] for a bald correct answer in K. Finds solution. Allow an ECF from MP2 if unit not converted, ie candidate uses 21m3 and
obtains 7.7 K
Do not penalise use of “°K”
iii
«models used to»
predict/hypothesize / lead to further theories
Response needs to identify two different reasons. ( N.B. only one in SL).
explain / help with understanding / help to visualize
Do not allow any response that is gas specific. The question is couched in general, nature of science terms and must be answered as
such.
simulate
simplify/approximate
Examiners report
[N/A]
8.
Which of the following is not an assumption of the kinetic model of ideal gases?
A. All particles in the gas have the same mass.
B. All particles in the gas have the same speed.
C. The duration of collisions between particles is very short.
D. Collisions with the walls of the container are elastic.
Markscheme
B
Examiners report
[N/A]
[1 mark]
9.
Under what conditions of density and pressure is a real gas best described by the equation of state for an ideal gas?
[1 mark]
A. Low density and low pressure
B. Low density and high pressure
C. High density and low pressure
D. High density and high pressure
Markscheme
A
Examiners report
[N/A]
10. An ideal gas and a solid of the same substance are at the same temperature. The average kinetic energy of the gas molecules is Eg[1 mark]
and the average kinetic energy of the solid molecules is Es. What is the comparison between Eg and Eg?
A.
Eg is less than Es.
B.
Eg equals Es.
C.
Eg is greater than Es.
D.
The relationship between Eg and Es cannot be determined.
Markscheme
B
Examiners report
[N/A]
11.
In the kinetic model of an ideal gas, which of the following is not assumed?
[1 mark]
A. The molecules collide elastically.
B. The kinetic energy of a given molecule is constant.
C. The time taken for a molecular collision is much less than the time between collisions.
D. The intermolecular potential energy of the molecules is zero.
Markscheme
B
Examiners report
[N/A]
12. What is the definition of the mole?
A. The amount of substance that has the same mass as 6.02 ×
[1 mark]
10 23
atoms of carbon-12.
B. The amount of substance that contains as many nuclei as the number of nuclei in 12 g of carbon-12.
C. The amount of substance that has the same mass as one atom of carbon-12.
D. The amount of substance that contains as many elementary entities as the number of atoms in 12 g of carbon-12.
Markscheme
D
Examiners report
[N/A]
13. A fixed mass of an ideal gas has a constant volume. Two quantities, R and S, of the gas vary as shown by the graph below.
What quantities do R and S represent?
[1 mark]
Markscheme
D
Examiners report
[N/A]
14.
What are the conditions of temperature and pressure at which the behaviour of a real gas approximates to the behaviour of an ideal [1 mark]
gas?
A. Low pressure and low temperature
B. Low pressure and high temperature
C. High pressure and low temperature
D. High pressure and high temperature
Markscheme
B
Examiners report
[N/A]
This question is about an ideal gas.
15a. Describe how the ideal gas constant R is defined.
[2 marks]
Markscheme
defined from the equation of state of an ideal gas PV=nRT;
all symbols (PVnT) correctly identified;
Examiners report
[N/A]
15b.
Calculate the temperature of 0.100 mol of an ideal gas kept in a cylinder of volume 1.40×10 –3 m 3 at a pressure of 2.32×10 5 Pa.
[1 mark]
Markscheme
390/391 K;
Examiners report
[N/A]
[2 marks]
15c. The gas in (b) is kept in the cylinder by a freely moving piston. The gas is now heated at constant pressure until the volume
occupied by the gas is 3.60×10–3 m 3. The increase in internal energy of the gas is 760 J. Determine the thermal energy given to the gas.
Markscheme
work done = (PΔV = 2.32 × 105 × 2.20 × 10−3 =) 510J;
thermal energy = (760 + 510 =) 1.27 × 103J;
Award [1 max] if volume is taken as 3.6×10–3, giving an answer of 1600 J.
Examiners report
[N/A]
15d.
After heating, the gas is compressed rapidly to its original volume in (b). Outline why this compression approximates to an
adiabatic change of state of the gas.
Markscheme
an adiabatic change is one in which no (thermal/heat) energy is transferred between system and surroundings / no energy
enters/leaves system;
a rapid compression means that there is insufficient time (for energy transfer) / OWTTE;
Examiners report
[N/A]
[2 marks]
This question is about internal energy and thermal energy (heat).
16a. Distinguish between internal energy and thermal energy.
[3 marks]
Markscheme
internal energy is the total kinetic and potential energy of the molecules of a body;
thermal energy is a (net) amount of energy transferred between two bodies;
at different temperatures;
Examiners report
Few could repeat the Subject Guide definition of internal energy and relate it to that of the molecules or atoms of the substance under
discussion. Understanding of thermal energy was very limited with a widespread failure to describe it in terms of transferred energy.
Candidates evidently struggle with this concept.
16b. Describe, with reference to the energy of the molecules, the difference in internal energy of a piece of iron and the internal energy [2 marks]
of an ideal gas.
Markscheme
the internal energy of the iron is equal to the total KE plus PE of the molecules; the molecules of an ideal gas have only KE so internal
energy is the total KE of the molecules;
Examiners report
The distinction between internal energy of a solid and an ideal gas is not well understood by candidates. The emphasis is on the word
“ideal” where no potential energy issues arise. Candidates were poor in their descriptions and explanations.
16c. A piece of iron is placed in a kiln until it reaches the temperature θ of the kiln. The iron is then quickly transferred to water held in a [4 marks]
thermally insulated container. The water is stirred until it reaches a steady temperature. The following data are available.
Thermal capacity of the piece of iron = 60JK–1
Thermal capacity of the water = 2.0×103JK–1
Initial temperature of the water = 16°C
Final temperature of the water = 45°C
The thermal capacity of the container and insulation is negligible.
(i) State an expression, in terms of θ and the above data, for the energy transfer of the iron in cooling from the temperature of the kiln to the
final temperature of the water.
(ii) Calculate the increase in internal energy of the water as the iron cools in the water.
(iii) Use your answers to (c)(i) and (c)(ii) to determine θ .
Markscheme
(i) 60×[θ −45];
(ii) (2.0×103×29)=5.8×104J;
(iii) 60×[ θ −45]=5.8×104;
θ =1000°C; (allow 1010°C to 3 sig fig )
Examiners report
The three sub-sections of this question led towards a determination of the final energy when iron at high temperature is added to cold
water in a container. There was confusion over both units and ideas. In (i) both K and °C appeared, in (ii) many answers of 29°C were
presented for the increase in the internal energy of the water, and in (iii) there were further errors in temperature units and significant
errors. Only about half the candidates were able to work towards a full answer in (iii).
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