Determination of the Latent Heat of Vaporization of Nitrogen - Lab Report Example

Temperature is an integral variable in any state of matter.  The temperature changes of an object can be used to calculate the heat capacity and specific heat capacity of any object.

Theory:

            The heat capacity is the amount of heat energy required to raise the temperature of a unit mass of an object by one degree.  The specific heat capacity is the amount of heat energy needed to raise the temperature of one gram of material by one degree. Two objects with different temperatures exchange heat, resulting in a temperature that is balanced between the two objects. The heat energy that is lost by the hotter object is absorbed by the object with the lower temperature.

            Calculating specific heat capacities involves the use of a calorimeter and a known mass of water. The calorimeter is designed in such a way that heat is not lost to or gained from the surrounding air (Laider). Since no heat is lost, then it can be safely assumed that heat lost or gained by the object inside the calorimeter is the same as the heat lost or gained by the water contained in the calorimeter.

            The change in heat energy (ΔQ), mass (m), specific heat (C), and temperature (T) are linked by the equation:

ΔQ = mCΔT

Using electrical power, P:

P = I = IV

E = Pt = IVt

Therefore: ΔQ = ΔE

And ΔQ = kΔE = kIVt

For nitrogen: ΔQ = ΔmLN2 ΔLN2

IV = (1/k)( ΔmLN2/Δt)LLN2

Procedure:

            A known mass of water was heated using an electrical heating wire. The initial and final temperatures of the water were measured and recorded, as well as the current, voltage, and the time that the electric switch was turned on.

            For liquid nitrogen, a known amount of heat was applied to liquid nitrogen. The quantity of liquid nitrogen that boiled away was measured by finding the difference between the initial and final masses. The flask with the liquid nitrogen was placed on a balance and the electrical heater lowered into the liquid nitrogen. The vaporization rate of the liquid nitrogen was measured after every ten seconds and recorded.

Data:

• For water:

Mass of water (kg)

time before

time after

ΔT

m c+w (kg)

m cup (kg)

time (s)

IVT/ΔT

0.29

22.6

57

34.4

0.545

0.255

300

1460.46977

0.203

28.7

76.5

47.8

0.458

0.255

300

1051.04937

0.19

29.2

74.6

45.4

0.445

0.255

300

1106.61145

0.12

30.1

93.2

63.1

0.375

0.255

300

796.199049

0.083

29.3

91.9

62.6

0.338

0.255

300

802.558466

                Temperature (T) was plotted against time. The temperature change was then used in the calculation of Cwater. (IVT)/ ΔT was plotted against the mass of water. The slope of the curve was found to be Cwater:

            Solving for the slope of the curve: y=3302x+458.1

                        Slope = 3302. Therefore, Cwater = 3302 /1000

                                                           A water = 3.302 J/g⁰C

            For liquid nitrogen, E = ΔE= IVt and Heat = ΔQ = Δmol. Thus IVt = ΔmL

            Measuring Δ in mass every 10 seconds and recording, the graph below was drawn. The slope begins and ends at the point when the switch was turned on and off respectively:

                From (IVT)/ ΔT, the value of IVT can be calculated by replacing ΔT in the equation (IVT)/ ΔT with the value in the table that corresponds to ΔT and then solving for (IVT). This gives a value of 50240.1601.           

                Using the formula LN2 = IVt / Δm yields the latent heat of vaporization of liquid nitrogen:

                        LN2 = 50240.1601 / Δm

                        LN2 =50240.1601 / (121.3-7.2)

                        LN2 = 440.316 /10

                        LN2 = 44.0316 cal/gram

Conclusion:

The specific heat capacity of water of successfully determined, along with the latent heat of vaporization for liquid nitrogen.
Future experiments can avoid these by diligently taking measurements and carefully setting up the calorimeter to ensure that no heat is lost to the surrounding.