Quantitative Thermal Conductivity and Heat Transfer

Thermal Conductivity 

Today we determined the conductivity of an aluminum can by explaining what variables are needed to find the value and the means of how the transfer of heat occurs through contact. The experiment used to determine was by placing probes in cold water in can and hot water surrounding the can with the same amount of water. As the temperature equaled, the slope was found to use a Q and then finding the variable k by using thickness, surface area, material and temperature of water. The whole day was related temperature, heat, and the specific heat capacity of different materials like aluminum. There was also the way heat and temperature passes through layers of materials and how Q, heat will be the same throughout a whole system.

The graph of the can in the water finding an average temperature and use the slope.
 

The way we found the dQ/dt was by using the slope value of the graph because it was the change in temperature, as the value Q, then we had to incorporate the surface area of the can along the thickness of the sides of the can, and lastly placed into the equation to find the value of k which to us was 6.44*10^-4 W . The heat is the on being transferred from the inside to the outside resulting in the amount of energy to reach an average temperature from the hot to cold. 

Our group's decision to what determines, like the variables, the amount of heat transfers out of the aluminum can.

This is the group's work on determining the value of the constant k from the equation given of dQ/dt.  

The method I used to determine the uncertainty of the value of k was by the percentage error of the amount our value came from the actual value which was 401. The value that we calculated was off by a significant amount of percentage due to wrong calculations in one of the variables that was used in the equation. In order to find the uncertainty value is to find the half of the difference between the values of the largest and smallest possibilities and finding the average. We were trying to find the range between the values close to 400.

 

Heat Transfer





The actual value of power of the immersion heater was 292.8 W and with the time of 20 seconds we were able to 5856 J of Heat. In this experiment we placed an immersion heater into water with a temp probe to determine the amount of heat energy needed to increase the temperature of the water under a time limit of 20 seconds.
The work showing the use of specific heat capacity q=mcT by using all the values we had, the final temp - initial temp, and the mass of the water being .200 kg resulting in 5447 J then dividing by time to find the actual amount of power used to increase the temperature which was 272.35 W.


Graph of Temperature vs Time, showing the increase in temperature from the initial one in the 20 second segment and found the slope to be around 0.364 C/s

The group's calculation of the experimental Power used to heat up the water, using the mass, the specific heat of water, and the change in temperature to find heat. Then divided by the amount of time.

The materials used to conduct the experiment of specific heat capacity of water by using temperature probes, Styrofoam cups, and immersion heater.

It is the graph of Heat vs Temperature and also of graph of Temperature vs Time from the experiment.









The graph showing Heat vs Temperature, showing its linear relationship between each other.








The physical meaning of the slope pertaining to the Heat per unit Mass vs Temperature is the amount of the heat energy that is used to increase by 1 gram of temperature of water in which our slope was off by having a slope of 1 in a linear fit. However that is the meaning of the slope which is the specific heat capacity of water.