5. Hot-air balloons rise because air expands when heated. During the 18th century Jacques Charles, Joseph...

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5. Hot-air balloons rise because air expands when heated. During the 18th century Jacques Charles, Joseph Louis Gay-Lussac, and others investigated the effect of increasing the temperature on the volume of a gas (at constant pressure). The table below lists the volume of an air sample at increasing temperatures. Volume 200 b. Temperature (C) 0 20 40 60 80 Volume (mL) 152.5 163.7 174.9 186.0 197.2 100 -200 -100 Temperature 100 200 A scatterplot of this data reveals a linear relationship between temperature and volume. a. Find a line that approximates the data. Note: the TI-84 Calculator can be used to find the line of best fit. To begin, you need to enter the data into the list editor. To enter the data press STAT 1 to get the list editor. Position the cursor with the arrow keys and enter the list of temperatures into list L, and the corresponding volume figures into list L. To use the calculator to determine the equation of the line of best fit (the linear regression equation), press STAT 4 ENTER y = ax + b Y=0.5585x +152.5 Use the equation of the line of best fit to estimate the volume of the air sample at 30C. 0.55 85130) + 152.52 169.275 mL 3 C. Find the temperature at which the volume is 180 mL. 180 =0.55 85 +152.52 490 What change in volume is brought about by a one-degree change in temperature? DV=? when st=1 What change in temperature would cause a one-mL change in volume? st = ? when AV=1 Assuming the horizontal axis represents temperature figures, find the horizontal intercept of the line of best fit. What is the physical significance of this result? See PSIHINTS 5. Hot-air balloons rise because air expands when heated. During the 18th century Jacques Charles, Joseph Louis Gay-Lussac, and others investigated the effect of increasing the temperature on the volume of a gas (at constant pressure). The table below lists the volume of an air sample at increasing temperatures. Volume 200 b. Temperature (C) 0 20 40 60 80 Volume (mL) 152.5 163.7 174.9 186.0 197.2 100 -200 -100 Temperature 100 200 A scatterplot of this data reveals a linear relationship between temperature and volume. a. Find a line that approximates the data. Note: the TI-84 Calculator can be used to find the line of best fit. To begin, you need to enter the data into the list editor. To enter the data press STAT 1 to get the list editor. Position the cursor with the arrow keys and enter the list of temperatures into list L, and the corresponding volume figures into list L. To use the calculator to determine the equation of the line of best fit (the linear regression equation), press STAT 4 ENTER y = ax + b Y=0.5585x +152.5 Use the equation of the line of best fit to estimate the volume of the air sample at 30C. 0.55 85130) + 152.52 169.275 mL 3 C. Find the temperature at which the volume is 180 mL. 180 =0.55 85 +152.52 490 What change in volume is brought about by a one-degree change in temperature? DV=? when st=1 What change in temperature would cause a one-mL change in volume? st = ? when AV=1 Assuming the horizontal axis represents temperature figures, find the horizontal intercept of the line of best fit. What is the physical significance of this result? See PSIHINTS