2. Aims
To determine the specific heat capacity ratio, γ,of air
with 30% humidity.
To determine the adiabatic lapse rate of air, methanol
and acetone at two different temperatures
2
3. What is an adiabatic process
An adiabatic process is one that occurs without the
transfer of heat between a thermodynamic system and
its surroundings. Q=0
Energy is transferred only as work.
This is achieved by:
1) Thermally Insulating the walls of the system
2) Having the process occur so quickly that no heat can be
exchanged.
3
4. What is an adiabatic process
Figure 1) Pressure v’s Volume graph for an Adiabatic process
4
5. Diesel engine
In a diesel engine, the
compression and expansion of
the pistons is so fast that no
heat can be lost.
During the adiabatic
compression, the temperature
rises.
This ignites the gas without
the piston without the need
for a spark plug unlike petrol
engines.
Figure 2) Diesel Engine
5
6. What is the specific heat
capacity ratio
The specific heat capacity ratio is defined as the heat
capacity at constant pressure divided by the heat
capacity at constant volume.
𝜸 =
𝒄 𝒑
𝒄 𝒗
It will be calculated by plotting calculated γ versus
compression time and extrapolating back to t = 0s.
6
7. Experimental Setup:
7
mounting
apparatus
60ml Plastic
syringe with gas
(covered in a towel
for part 2)
valve
pressure
transducer
thermistor
(internal)
power
supply
thermistor
(external)
automated
bridge
circuit
saturated cotton bud
with acetone or
methanol (part 2)
analog to digital
converter
Figure 3) setup of the complete circuit
8. Difference between a rapid (<1.0s)
and a slow (>1.0s) compression:
80000
100000
120000
140000
160000
180000
200000
220000
65 66 67 68 69 70 71 72 73
Pressure(Pa)
Time (s)
Pressure (Pa) v's Time (s)
P1
P2
P3
80000
100000
120000
140000
160000
180000
200000
220000
55 56 57 58 59 60 61 62 63
Pressure(Pa) Time (s)
Pressure (Pa) v's Time (s)
P2, P3
P1
Figure 5) graph of pressure v’s time for a slow
compression time (~3.0s)
Figure 4) graph of pressure v’s time for a rapid
compression time (~0.35s)
8
9. Difference between a rapid (<1.0s)
and a slow (>1.0s) compression:
22.6
22.8
23
23.2
23.4
23.6
23.8
24
65 66 67 68 69 70 71 72 73
Temperature(degC)
Time (s)
Temperature (deg C) v's Time (s)
T2
T1
T3
22.6
22.8
23
23.2
23.4
23.6
23.8
24
55 56 57 58 59 60 61 62 63Temperature(degC)
Time (s)
Temperature (deg C) v's Time (s)
T1
T2 T3
Figure 7) graph of temperature v’s time
for a slow compression time (~3.0s)
Figure 6) graph of temperature v’s time
for a rapid compression time (~0.35s)
9
10. Graph of γ versus compression time
for compression times 0.0s – 7.0s
y = 0.0125x2 - 0.1164x + 1.2785
R² = 0.7534
0.9
1
1.1
1.2
1.3
1.4
1.5
-1 0 1 2 3 4 5 6 7 8
specificheatratio,γ
compression time (s)
specific heat ratio v's compression time (s)
Figure 8) γ v’s compression time for 0.0s - 7.0s
10
11. Graph of γ versus compression time
for compression times 0.0s – 1.0s
y = 0.087x2 - 0.3243x + 1.347
R² = 0.3316
1.0
1.1
1.1
1.2
1.2
1.3
1.3
1.4
1.4
1.5
-0.2 0 0.2 0.4 0.6 0.8 1
specificheatratio,γ
compression time (s)
specific heat ratio v's compression time (s)
Figure 9) γ v’s compression time for 0.0s - 1.0s
11
12. Graph of γ versus compression time
for compression times 0.0s – 0.5s
y = 0.907x2 - 0.85x + 1.4162
R² = 0.2315
1.0
1.1
1.1
1.2
1.2
1.3
1.3
1.4
1.4
1.5
1.5
-0.1 0 0.1 0.2 0.3 0.4 0.5
specificheatratio,γ
compression time (s)
specific heat ratio v's compression time (s)
Figure 10) γ v’s compression time for 0.0s - 0.5s
12
13. Graphs of γ as a function of compression
time for various compression time ranges:
13
y = 0.0125x2 - 0.1164x + 1.2785
R² = 0.7534
0.9
1
1.1
1.2
1.3
1.4
1.5
-2 0 2 4 6 8
specificheatratio,γ
compression time (s)
specific heat ratio v's
compression time (s)
y = 0.087x2 - 0.3243x + 1.347
R² = 0.3316
1.0
1.1
1.2
1.3
1.4
1.5
-0.2 0 0.2 0.4 0.6 0.8 1
specificheatratio,γ
compression time (s)
specific heat ratio v's
compression time (s)
Figure 8) γ v’s compression time for 0.0s - 7.0s Figure 9) γ v’s compression time for 0.0s - 1.0s
y = 0.907x2 - 0.85x + 1.4162
R² = 0.2315
1.0
1.1
1.2
1.3
1.4
1.5
-0.1 0 0.1 0.2 0.3 0.4 0.5
specificheatratio,γ
compression time (s)
specific heat ratio v's
compression time (s)
Figure 10) γ v’s compression time for 0.0s - 0.5s
14. Specific heat capacity ratio
results
The most accurate value obtained was from the 0.0s-
0.5s compression time range. The γ value obtained was
1.416.
The theoretical γ value is 1.4
The error on the calculated value was 3.66%
Calculated γ = 1.416 ± 0.052
14
15. What is the adiabatic lapse rate
The adiabatic lapse rate is the change in temperature T divided by the
change in pressure P at constant entropy S.
Г =
𝝏𝑻
𝝏𝑷 S
This equation can be modified to incorporate height in the atmosphere(z)
Г =
𝝏𝑻
𝝏𝒛 S
It is defined as the rate of decrease in temperature (T) of a parcel of air
as it moves upwards (z) without exchanging heat with its surroundings.
This process takes place in the troposphere.
15
16. Adiabatic lapse rate
16
The reason for this difference is that latent heat is
released when water condenses, leading to a decrease
in the rate of temperature drop as altitude increases.
There are two types of adiabatic lapse rates, a
dry and a saturated adiabatic lapse rate.
Figure 11) diagram of the adiabatic lapse rate in the atmosphere
Dry adiabatic lapse rate =
9.8 K/km
Saturated adiabatic lapse
rate = 5 K/km
17. Adiabatic lapse rate impact
It is the reason relief rain occurs
It is why we can get snow covered mountain tops in warm
countries
Figure 12) diagram of the adiabatic lapse rate in the atmosphere
Mount Kilimanjaro in Tanzania (5900 meters)
Mean annual temperature at the top of -7 ⁰C
Tanzania has temperatures typically above 17 ⁰C throughout
the year
17
18. Experimental Hot towel
Small sample of volatile liquid was added (methanol,
acetone)
It was allowed to vaporised
It was then compressed
Graphs of change in temperature as a function of
change in pressure were plotted
The slopes were used to obtain the trend of the
adiabatic lapse rate.
Figure 13) experimental setup used to determine the adiabatic lapse rate
18
19. Graphs of the compression of
Acetone at room temperature
dT ≈ 3⁰C
dP ≈ 1x10e5 Pa
Figure 15) graph of temperature v’s time for acetone
vapour at room temperature
Figure 14) graph of pressure v’s time for acetone vapour at
room temperature
19
20. Graphs of the compression of
Acetone at a higher temperature
dT ≈ 4⁰C
dP ≈ 1.25x10e5 Pa
Figure 17) graph of temperature v’s time for acetone vapour at
a higher temperature
Figure 16) graph of pressure v’s time for acetone vapour at a
higher temperature
20
21. Adiabatic lapse rate for
acetone higher temperature
y = 9.44E-05x - 3.39E+00
R² = 7.60E-01
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
65000 67000 69000 71000 73000 75000 77000
ChangeoftemperaturedT(K)
Change of pressure dP (Pa)
dT versus dP for acetone at a higher temperature
Figure 18) graph of change in temperature v’s change in
pressure for acetone vapour at a higher temperature 21
22. Summary of adiabatic lapse
rates
Room Temperature Γ ( K Pa-1) ‘Hot Towel’ Temperature Γ ( K Pa-1)
Air 1.77x10-5 ± 8.43x10-7 1.56x10-5 ± 7.43x10-7
Methanol 2.08x10-5 ± 9.90x10-7 3.07x10-5 ± 1.46x10-6
Acetone 2.73x10-5 ± 1.30x10-6 9.44x10-5 ± 4.19x10-6
The adiabatic lapse rates increase with
saturation, however they should decrease?
Re-evaluate theory
Table 1) Table of results of adiabatic lapse rates
22
23. PV diagram for an adiabatic
compression in the troposphere
𝜕T
𝜕P S
Figure 19) PV diagram for adiabatic compression in the
atmosphere
23
24. PV diagram for the
compression in the syringe
𝜕T
𝜕V s
Figure 20) PV diagram for adiabatic compression in the
atmosphere
24
25. PV diagram analyse
Two different processes occur
Through manipulation of
𝜕T
𝜕V s
we find a new
relationship between the data obtained and the
adiabatic lapse rate
Γ = −
V
γP
𝜕T
𝜕V s
25
26. Conclusion
Determined the specific heat capacity ratio of air with
30% humidity to within the margin of error
Determined intermediate values which may be used to
calculate the adiabatic lapse rate
26
