5.) Use your curve-fit equation to predict (calculate) the pressure at given temperatures outside the range of the experiment. Show your work for at least one of the calculations in your report. Pressure at 200 K Pressure at 400 K Y = 0.345x - 21.6 kPa kPa
Added by Luis Miguel P.
Close
Step 1
345x - 21.6 Given x = 200K, substitute x into the equation: Y = 0.345(200) - 21.6 Y = 69 - 21.6 Y = 47.4 Therefore, the predicted pressure at 200K is 47.4 kPa. Show more…
Show all steps
Your feedback will help us improve your experience
Carson Merrill and 60 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Modeling Data The table shows the temperatures $T\left(^{\circ} \mathrm{F}\right)$ at which water boils at selected pressures $p$ (pounds per square inch). (Source: Standard Handbook of Mechanical Engineers) $$\begin{array}{|c|c|c|c|c|} \hline p & 5 & 10 & 14.696(1 \mathrm{atm}) & 20 \\ \hline T & 162.24^{\circ} & 193.21^{\circ} & 212.00^{\circ} & 227.96^{\circ} \\ \hline \end{array}$$ $$\begin{array}{|c|c|c|c|c|c|} \hline p & 30 & 40 & 60 & 80 & 100 \\ \hline T & 250.33^{\circ} & 267.25^{\circ} & 292.71^{\circ} & 312.03^{\circ} & 327.81^{\circ} \\ \hline \end{array}$$ A model that approximates the data is $T=87.97+34.96 \ln p+7.91 \sqrt{p}$ (a) Use a graphing utility to plot the data and graph the model. (b) Find the rates of change of $T$ with respect to $p$ when $p=10$ and $p=70$
Differentiation
The Chain Rule
Experiment DATA ANALYSIS: The Pair for Trials 3-6 must be calculated because the temperatures were increased. As you warmed the flask, the air in the flask exerted pressure that you must calculate. Use the gas law relationship shown below to complete the calculations. Remember that all gas law calculations require Kelvin temperature. Use the Pair from Trial 1 as P1 and the Kelvin temperature of Trial 1 as T1. Calculate and record the Pvap for each trial by subtracting Pair from Ptotal.
Adi S.
Modeling Data The table shows the temperatures $T$ (in $^{\circ} \mathrm{F}$ ) at which water boils at selected pressures $p$ (in pounds per square inch). A model that approximates the data is $$T=87.97+34.96 \ln p+7.91 \sqrt{p}$$ (a) Use a graphing utility to plot the data and graph the model. (b) Find the rates of change of $T$ with respect to $p$ when $$p=10$ and $p=70 .$$ (c) Use a graphing utility to graph $T^{\prime}$ . Find $\lim _{p \rightarrow \infty} T^{\prime}(p)$ and interpret the result in the context of the problem.
Logarithmic, Exponential, and Other Transcendental Functions
The Natural Logarithmic Function: Differentiation
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD