lab 2 thermal brand new

4
Lab 2 Expansion process of an ideal gas Aim Objectives 1) To apply the principle of mass balance and the ideal gas equation to determine the ratio of volumes of the two vessels and prove that the equations hold for real g ases at approximately atmospheric pressure 2) To investigate the properties of an ideal gas, the principle of mass balance by determining the heat capacity ratio k = C p /C v for air. Also to examine other thermodynamic properties by using P-V-T data Objective (2) Results Group 1 2 3 4 5 Patm (kPa) 101.63 101.62 101.67 101.67 101.62 Tamb (°C) 31.5 31.8 31.8 31.8 31.7 P1 (gauge) (kPa) 31.37 28.33 28.55 28.63 32.8 P1 (abs) (kPa) 133 129.95 130.22 130.3 134.42 T1 (°C) 31.3 31.6 31.6 31.5 31.5 P2 (gauge) (kPa) 10.12 9.04 10 6.15 19.9 P2 (abs)(kPa) 91.51 92.58 91.67 95.52 81.72 T2 (°C) 37.8 37 36.7 37.4 35.43 P3 (gauge) (kPa) 5.45 4.92 4.92 3.96 19.29 P3 (abs) (kPa) 96.18 96.7 96.75 97.71 82.33 T3 (°C) 31.6 31.7 31.8 31.7 31.6 experimental k 1.126833243 1.12391 1.151778 1.067199 1.011711 real k 1.394532034 1.39431 1.394264 1.394655 1.395212 T2(ohms) 1147 1050 1030 1203 1291 T2 (C) from ohms 39.28205128 41.76923 42.28205 37.91111 36 T2 K 312.4320513 314.9192 315.4321 311.0611 309.15

Upload: ku-ashman-ku-aziz

Post on 05-Apr-2018

215 views

Category:

Documents


0 download

TRANSCRIPT

8/2/2019 Lab 2 Thermal Brand New

http://slidepdf.com/reader/full/lab-2-thermal-brand-new 1/4

Lab 2

Expansion process of an ideal gas

Aim

Objectives

1)  To apply the principle of mass balance and the ideal gas equation to determine the ratio of 

volumes of the two vessels and prove that the equations hold for real gases at

approximately atmospheric pressure

2)  To investigate the properties of an ideal gas, the principle of mass balance by determining

the heat capacity ratio k = Cp/Cv for air. Also to examine other thermodynamic properties

by using P-V-T data

Objective (2)

Results

Group 1 2 3 4 5

Patm (kPa) 101.63 101.62 101.67 101.67 101.62

Tamb (°C) 31.5 31.8 31.8 31.8 31.7

P1 (gauge)

(kPa) 31.37 28.33 28.55 28.63 32.8

P1 (abs) (kPa) 133 129.95 130.22 130.3 134.42

T1 (°C) 31.3 31.6 31.6 31.5 31.5

P2 (gauge)

(kPa) 10.12 9.04 10 6.15 19.9

P2 (abs)(kPa) 91.51 92.58 91.67 95.52 81.72

T2 (°C) 37.8 37 36.7 37.4 35.43

P3 (gauge)

(kPa) 5.45 4.92 4.92 3.96 19.29

P3 (abs) (kPa) 96.18 96.7 96.75 97.71 82.33

T3 (°C) 31.6 31.7 31.8 31.7 31.6

experimental k 1.126833243 1.12391 1.151778 1.067199 1.011711

real k 1.394532034 1.39431 1.394264 1.394655 1.395212

T2(ohms) 1147 1050 1030 1203 1291

T2 (C) from

ohms 39.28205128 41.76923 42.28205 37.91111 36

T2 K 312.4320513 314.9192 315.4321 311.0611 309.15

8/2/2019 Lab 2 Thermal Brand New

http://slidepdf.com/reader/full/lab-2-thermal-brand-new 2/4

Discussions

Why is it necessary to measure the pressure and temperature of state 3?

Equation 1

() 

According to the equation above, the k value can be calculated using the state 1 and state 2 values.

However, the mass of the air is unknown since the mass of the air could not be calculated

accurately. To minimise the error, it was necessary to measure state 3 values which allowed the use

of the following equation

Equation 2

 

See the appendix for the derivation from equation 1 to equation 2 .

The advantages and disadvantages

One of the advantages of having state 3 values is that , pressure value could be measured directly

which minimised error whereas if the mass had been calculated from states 1 and 2 using an

approximate value for the density of air and the ideal gas equation, more sources of error would

have been introduced to our experimental k value.

A disadvantage of using the state 3 pressure is that the point where thermal equilibrium is achieved

is not accurately known. For example the two temperature readings for vessels 1 and 2 were not

exactly equal. This introduces further errors into the experimental k value.

Why does the temperature change from state 1 to state 2?

We are assuming the process is adiabatic (Q=0) because the transition from state 1 to state 2

happens very rapidly. There fore the increase in temperature is a result of flow work done when

additional moles of air flow into the vessel.

Determining experimental k:

We calculated experimental k values using equation 2 above. The values for pressures were

calculated by adding (vessel 1) or subtracting (vessel 2) the gauge pressure from the atmospheric

pressure. The results are shown in the table above.

The average experimental k value can be calculated to be 1.0963.

Determining theoretical k value using the following equation;

 

   

8/2/2019 Lab 2 Thermal Brand New

http://slidepdf.com/reader/full/lab-2-thermal-brand-new 3/4

A = 3.355, B= 0.575 x 10^-3 and D = -0.016 x 10^5 as given in the lab manual . The temperature

used in the calculation is Tamb . 

The average theoretical value was calculated to be 1.3946.

Conclusion

The theoretical value of k was calculated to be 1.3946 and the experimental value of k was

calculated to be 1.0963. The percentage difference is (1.3946-1.0963) / 1.3946 is 21.4 %.

The error could have sourced from

1)  In the transition from state 1 to state 2 , we assumed it was adiabatic process where all

the flow work of the air was transferred to the system and none to the surrounding . (

Q= 0). In reality, Q is not zero since a small amount of heat was transferred to the

surrounding. This resulted in lower k experimental value than expected since lower

energy than expected was retained by the system. Since only partial energy being

transferred to the vessel, it means that less enthalpy carried to the vessel by air. Since

enthalpy is directly proportional to specific heat capacity at constant pressure, Cp , the

lower the enthalpy, the lower the Cp. As a result, the experimental value of k is less

than the theoretical value of k.

2)  The time intervals were 1 second apart which makes it very hard to record the exact

value of the temperature 2.

3)  The assumption was made that the gas was in ideal state.

Objective 1

Results

1 2 3 4 5

P1,i (abs) (kPa) 130.05 131.14 131.62 130.14 131.54

T1,i (K) 305.2 305.2 305.33 304.91 305.25

P2,i (abs) (kPa) 66.63 66.63 66.6 66.65 90.15

T2,i (K) 304.55 304.45 304.55 304.3 305.25

P1,f (abs) (kPa) 109.61 109.96 110.17 109.61 119.59

T1,f (K) 305.06 305.02 305.15 304.69 305.2

P2,f (abs) (kPa) 109.41 109.96 110.15 109.6 119.47T2,f (K) 305.15 304.95 305.15 304.8 305.25

V2/V1 0.478006 0.488143 0.492239 0.4772 0.406903

8/2/2019 Lab 2 Thermal Brand New

http://slidepdf.com/reader/full/lab-2-thermal-brand-new 4/4

Discussions

How to determine the volume of two vessels from the principle of mass balance?

By assuming the air as an ideal gas and applying it to the mass balance equation of 

M1 initial – M1 final = M2 final – M2 initial

We can obtain equation 3 =

The long equation for objective 1

Why the density mass relationship equation is not used to determine the volume of the two

vessels?

Instead of using the equation 3, the volume of the vessel can be calculated by just simply dividingthe mass of the air in the vessel with the density of the air. However this method is not reliable as

the density of the air is not known and it is not practical to measure the mass of the air as it might

cause more error in the result.

Determining experimental volume ratio of small vessel to large vessel:

By substituting the data collected during experiment to the

Why does the temperature in vessel 1 drop while the temperature in vessel 2 increase at the final

state?

Conclusion

The theoretical ratio of small vessel to large vessel is 0.4063 and the average experimental ratio of 

small vessel to large vessel is 0.4685.The percentage difference is (0.4685-0.4063) / 0.4063 is 15.3 %.

The error could have sourced from

1)