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===== Analysis ===== | ===== Analysis ===== | ||

- | Calculate the work W done by turning the outer brass cup using equation 9.1. Calculate its error according to expression 1.3 and 1.7 in Lab1 from the errors of the effective diameter d of the disk and the force F. Calculate the temperature rise $\delta T$ of the system and its absolute error according to expression (1.6) from Lab 1. | + | Calculate the work W done by turning the outer brass cup using equation 10.1. Calculate its error according to expression 1.3 and 1.7 in Lab1 from the errors of the effective diameter d of the disk and the force F. Calculate the temperature rise $\delta T$ of the system and its absolute error according to expression (1.6) from Lab 1. |

In this experiment, the generated heat is absorbed not just by one single material, it is absorbed by 4 different elements: the water, the brass cups, the stirring rod, and the thermometer. In order to calculate the total heat generated in this system, you use equation 8.2 for each of the elements. Assume that the stirring rod is made of aluminum and the thermometer is made of glass. The specific heats //c// of these materials are provided in the table below. | In this experiment, the generated heat is absorbed not just by one single material, it is absorbed by 4 different elements: the water, the brass cups, the stirring rod, and the thermometer. In order to calculate the total heat generated in this system, you use equation 8.2 for each of the elements. Assume that the stirring rod is made of aluminum and the thermometer is made of glass. The specific heats //c// of these materials are provided in the table below. | ||

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|glass (thermometer)|0.200| | |glass (thermometer)|0.200| | ||

- | Calculate the heat absorbed by the water, Q<sub>w</sub> , using equation 9.2. Repeat the calculations for the brass cups, stirring rod, and the thermometer. Record these values on your worksheet. Calculate the total heat Q by taking the sum of the heat absorbed by each of the four elements. You should see that the main contributions to the overall absorbed heat are from the brass cups and the water. The relative errors in the masses of both the brass cups and the water are fairly small, so we can consider only the error in our change of temperature ($\delta T$) when calculating the error in Q. Therefore, we can find the absolute error in Q simply by mutliplying it by the relative error in $\delta T$. | + | Calculate the heat absorbed by the water, Q<sub>w</sub> , using equation 10.2. Repeat the calculations for the brass cups, stirring rod, and the thermometer. Record these values on your worksheet. Calculate the total heat Q by taking the sum of the heat absorbed by each of the four elements. You should see that the main contributions to the overall absorbed heat are from the brass cups and the water. The relative errors in the masses of both the brass cups and the water are fairly small, so we can consider only the error in our change of temperature ($\delta T$) when calculating the error in Q. Therefore, we can find the absolute error in Q simply by mutliplying it by the relative error in $\delta T$. |

Calculate your experimental proportionality constant between the heat unit of the calorie and the energy unit of the Joule by calculating $\frac{W}{Q}$. Calculate the error for this ratio according to equations (1.3) and (1.7) from Lab1. Compare your measured value of $\frac{W}{Q}$ with the accepted value of 4.187 J/cal and check whether your measurement is consistent with it within expermental error. | Calculate your experimental proportionality constant between the heat unit of the calorie and the energy unit of the Joule by calculating $\frac{W}{Q}$. Calculate the error for this ratio according to equations (1.3) and (1.7) from Lab1. Compare your measured value of $\frac{W}{Q}$ with the accepted value of 4.187 J/cal and check whether your measurement is consistent with it within expermental error. |