Department of Biology, Fort Valley State University, Fort Valley, GA, United StatesĪ growing number of students are now opting for online classes.Would the slope of the graph for Helium be greater or less than the slope for air? Why?Ĥ. What is the ratio of specific heats of a monatomic gas in theory? Why?ģ. What is the ratio of specific heats of a diatomic gas in theory? Why?Ģ. Never attach a high pressure hose directly to the apparatus.ġ. Then the hose clamp is closed with the piston at 9 cm. NOTE: Another gas, such as Helium, can be introduced into the cylinder by moving the piston to its lowest position, attaching a rubber balloon filled with Helium to the unused port and opening the hose clamp and letting the Helium from the balloon flow into the cylinder, pushing the piston up to the top. If another gas is available, determine γ for that gas. Apply a linear fit and use the slope to calculate γ for air. Choose a QuickCalc of the period squared on the horizontal axis. Unless a barometer is available, assume the atmospheric pressure is 1.01 x 10 5 Pa. Then continue to lower the piston in steps of 1 cm, repeating the procedure at each piston position down to 1 cm. Loosen the side thumb screw and now the piston will stay at 8 cm. Lower the piston to the 8-cm mark and clamp it at this position with the side thumb screw at the top of the cylinder. Type this period and the corresponding piston height into the table.ĥ.
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Measure the period by measuring the time for several peaks and dividing by the number of peaks. Expand the area of the graph that shows the oscillation. Using the Coordinates Tool on the graph, determine the period of the oscillation from the pressure versus time graph. Using the tip of your finger, pluck the top of the piston. Click on Record in the PASCO Capstone program.ģ. Find the mass (m) of the piston (given on the apparatus label) and the cross-sectional area (A) of the piston (the piston diameter is given on the apparatus label).Ģ. Also, in a table, create a User-Entered Data measurement called “Piston Height” and another User-Entered Data measurement called “Period”.ġ. In PASCO Capstone, create a graph of Pressure vs. Plug the Dual Pressure Sensor into Channel A on the 850 interface. Loosen the side thumb screw and now the piston will stay at 9 cm. Raise the piston to the 9-cm mark and clamp it at this position with the side thumb screw at the top of the cylinder. Unclamp both of the tube clamps at the bottom of the apparatus. Slide the Heat Engine/Gas Laws Apparatus onto the rod stand as shown in Figure 1.Īttach a Dual Pressure Sensor to one of the ports on the Heat Engine Apparatus. Where m = mass of piston, A = cross-sectional area of piston, P = atmospheric pressure, and the slope is from the graph of h vs. Solving equation (12) for the ratio of specific heats gives Thus, if the piston height is plotted versus the square of the period, the resulting graph will be a straight line withĪnd y-intercept h o. Substituting in for the volume and solving for the height of the piston, h, gives The total volume is A(h+h o), where h is the height measured on the labeled scale and h o is the unknown height below zero on the label. Substituting into the period equation for k gives Taking a derivative of Equation (2) gives Thus the process is adiabatic andįor a diatomic gas, C V = 5/2 R and C P = 7/2 R, so γ= 7/5. To find a relationship between dP and dV, we assume that if the oscillations are small and rapid, no heat is gained or lost by the gas. The resulting force on the piston is given by F = (dP)A where dP is the small change in pressure. When the piston is displaced downward a distance x, the volume decreases by a very small amount compared to the total volume: dV = xA where A is the cross-sectional area of the piston. To determine the spring constant, k, for air, calculate the force when the piston is displaced a distance x. The period of oscillation of a mass on a spring (or for the piston and air) is
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The piston acts as the mass and the air acts as the spring. Just like a mass on a spring, the piston will oscillate.
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If the piston is displaced downwards a distance x, there will be a restoring force which forces the piston back toward the equilibrium position.
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Gamma, the ratio of specific heat, can be determined by measuring the period of oscillation. The piston will then oscillate about the equilibrium position. In Ruchhardt's Method, a cylinder of gas is compressed adiabatically by plucking the piston. The ratio of specific heat capacities is calculated using the period of oscillation, according to Ruchhardt's method. The oscillating pressure is recorded as a function of time and the period is determined. The piston is plucked by hand and allowed to oscillate. Ratio of Specific Heats of a Gas EX-5531 Page ofĪ cylinder is filled with air and a Pressure Sensor is attached.