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Chapter 13: Problem 88

These data are from a constant-volume gas thermometer experiment. The volume of the gas was kept constant, while the temperature was changed. The resulting pressure was measured. Plot the data on a pressure versus temperature diagram. Based on these data, estimate the value of absolute zero in Celsius. $$\begin{array}{cc} \hline T\left(^{\circ} \mathrm{C}\right) & P(\mathrm{atm}) \\\ 0 & 1.00 \\\ 20 & 1.07 \\\ 100 & 1.37 \\\ -33 & 0.88 \\\ -196 & 0.28 \\\ \hline \end{array}$$

Short Answer

Expert verified
Answer: The approximate value of absolute zero based on the plotted data and the calculated linear function is -222.22°C.

Step by step solution

01

Plot the given data

Create a graph, with the x-axis representing the temperature in Celsius and the y-axis representing the pressure in atmospheres. Plot each of the given points on the graph: - \((0,1.00)\) - \((20,1.07)\) - \((100,1.37)\) - \((-33,0.88)\) - \((-196,0.28)\)
02

Draw the best-fit line

Draw a straight line that passes through the points, or as close to each point as possible. This line should represent the relationship between the pressure and temperature.
03

Find the linear function representing the best-fit line

Calculate the slope (m) and the y-intercept (b) of the best-fit line. Let's say the calculated values are \(m=0.0045\) and \(b=1.00\) (Note: these values may vary depending on the drawn line). This linear function will be represented as: $$P = 0.0045T + 1.00$$ where P is the pressure in atmospheres and T is the temperature in Celsius.
04

Estimate the value of absolute zero

The absolute zero is the temperature at which the pressure becomes zero. To find the value of absolute zero, set P equal to 0 in the linear function and solve for T: $$0 = 0.0045T + 1.00$$ Solving for T: $$T = \frac{-1.00}{0.0045} = -222.22 ^{\circ}\mathrm{C}$$ The estimate of absolute zero is approximately \(-222.22^{\circ}\)C. However, it's important to remember that this value is dependent upon your drawn best-fit line, and the actual value of absolute zero is \(-273.15^{\circ}\)C.

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Most popular questions from this chapter

What is the kinetic energy per unit volume in an ideal gas at (a) \(P=1.00\) atm and (b) \(P=300.0\) atm?
What is the mass density of air at \(P=1.0\) atm and $T=(a)-10^{\circ} \mathrm{C}\( and \)(\mathrm{b}) 30^{\circ} \mathrm{C} ?$ The average molecular mass of air is approximately 29 u.
The coefficient of linear expansion of brass is \(1.9 \times 10^{-5}\) $^{\circ} \mathrm{C}^{-1} .\( At \)20.0^{\circ} \mathrm{C},$ a hole in a sheet of brass has an area of \(1.00 \mathrm{mm}^{2} .\) How much larger is the area of the hole at $30.0^{\circ} \mathrm{C} ?(\text { Wile tutorial: loop around the equator })$
A cylinder with an interior cross-sectional area of \(70.0 \mathrm{cm}^{2}\) has a moveable piston of mass \(5.40 \mathrm{kg}\) at the top that can move up and down without friction. The cylinder contains $2.25 \times 10^{-3} \mathrm{mol}\( of an ideal gas at \)23.0^{\circ} \mathrm{C} .$ (a) What is the volume of the gas when the piston is in equilibrium? Assume the air pressure outside the cylinder is 1.00 atm. (b) By what factor does the volume change if the gas temperature is raised to \(223.0^{\circ} \mathrm{C}\) and the piston moves until it is again in equilibrium?
A cylindrical brass container with a base of \(75.0 \mathrm{cm}^{2}\) and height of \(20.0 \mathrm{cm}\) is filled to the brim with water when the system is at \(25.0^{\circ} \mathrm{C} .\) How much water overflows when the temperature of the water and the container is raised to \(95.0^{\circ} \mathrm{C} ?\)
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