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Q. 60

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 546

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Short Answer

Your laboratory assignment for the week is to measure the specific heat ratio of carbon dioxide. The gas is contained in a cylinder with a movable piston and a thermometer. When the piston is withdrawn as far as possible, the cylinder's length is . You decide to push the piston in very rapidly by various amounts and, for each push, to measure the temperature of the carbon dioxide. Before each push, you withdraw the piston all the way and wait several minutes for the gas to come to the room temperature of . Your data are as follows:

Use the best-fit line of an appropriate graph to determine for carbon dioxide.

The best-fit line of an appropriate graph to determine for carbon dioxide is

See the step by step solution

Step by Step Solution

Step 1: Given Information

Cylinder length

Temperature

Given Data:

Step 2: Explanation

Since the process is adiabatic, we know that const. Therefore we can write

This allows us to express the ratio of pressures as

Rearranging the ideal gas law for the case when the number of moles is constant, we get

Having already expressed the ratio of pressures, we can write

Dividing both sides by the ratio of volumes and by the power rules, we can write

Step 3: Explanation

Having done this derivation, what we can do is find out the ratios for all the compression trials. Also, we must take note that the ratio of the volume will be equal to the ratio of the initial (total) length of the cylinder by the length it reaches. That is, our list of volumes, in units of , will be

By a similar manner, we can construct a list of temperatures in the experiments, giving the temperatures after the compression in units of . Considering that we must convert to Kelvin, we would have

Now we can plot the temperature ratios as a function of the volume ratios. After scattering, we can fit a power function and from that determine the parameter. A such graph is given below:

Step 4: Final Answer

Therefore, as we can see from the fitting parameters, we have

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