Desk Set
Desk Set
2 questions: If you pour a cup of coffee 200F, and put it on a table in a. …?
PLEASE SEE THE WORK: 1. If you pour a cup of coffee to 200F, and put it on a desk in a room that is 68F and 10 minutes later, 145F, which will temperatue 15 minutes after the originally served? 2. The krypton-91 radioactive substance has a very short half-life of about 10 seconds. What is the decay constant for this substance? (3 points)
1. Newton cooling law is a differential equation that can express simple time-dependent temperature, T (t), once the initial temperature of the object is t_0 known (in this case coffee), ambient temperature (room temperature) Ta is known, a temperature reading later known. and Newton's law of cooling, says that the rate of decrease in temperature is proportional to the difference in temperature and object temperature: dT / dt is proportional to (T-Ta) where Ta room temperature the object is constant and T is a temporary variable. Rewrite as: dT / dt =- k (T-Ta), k is the constant of proportionality (negative from cooling water). eachside Multiply by dt: dt =- k (T-Ta) dT dt / (T-Ta) dT =- k ∫ dt / (T-Ta) ln-k ∫ dt = (T-Ta) = c-+ kt e ^ ln (T-Ta) = E ^ (kt +-c) T-Ta = e ^ C * e ^ (-kt) T-Ta = c * e ^ (-kt) [c ^ e is any constant c] T (t) = Ta + c * e ^ (-kt) Notice There are two unknown The constants C and K. Must Use boundary conditions to solve for them. At t = 0, the object's temperature is a temperature T T0 (0) = T0 = Ta * c + e ^ (-k * 0) T (0) = T0 = Ta + Cc = T0-Ta The final equation is: • • • • • • • • • • • • • • • • • • • • • • • • • • • • • T (t) Ta = + (T0-Ta) * e ^ (-kt) • • • • • • • • • • • • • • • • • • • • • • • • • • • • • For your problem: T0 = 200 Ta = 68 T (10) = 145 T (15) =? T (t) = + Ta (T0-Ta) * e ^ (-kt) T (10) = 145 = 68 + (200-68) * e ^ (-k * 10) 77 = 132 * e ^ (-10k) 77 / 132 = e ^ (-10k) ln (77/132) =- k = 10k ln (77/132) / -10 k = 0.0538 T (t) = 132 * 68 + e ^ (-. 0538t) T (15) = 68 + 132 * e ^ (-. 0538 * 15) • • • • • • • • • • • • • • • • • • T (15) = 126.9 ° F • • • • • • • • • • • • • • • • • • 2. dN / dt is proportional to N, N = number of krypton dN / dt = kN, (k is the constant of proportionality – Negative and decaying) dN / N = ∫ KDT-dN / N =- KDT ∫ ln (N) C-kt + N = e ^ (-kt + = c) N = e ^ c * e ^ (- kt) N (t) = c * e ^ (-kt) Obtain C: N (0) = N0 = c * e ^ (-k * 0) N (0) = N0 = cc = N0 (initial amount of substance) • • • • • • • • • • • • • • • • • • N (t) = N0 * e ^ (-kt) • • • • • • • • • • • • • • • • • • From your information: N (10) = 1 / 2 N0 = N0 * e ^ (-K * 10) 1 / 2 = e ^ (-k * 10) (1 / 2) =- k * k = 10 – 1 / 10 * ln (1 / 2) k = 1 / 10 * ln (2) k = decay constant = 0.06931 • • • • • • • • • • • • • • • • • • • • • • • • N (t) = N0 * e ^ (-. 06931t) • • • • • • • • • • • • • • • • • • • • • • • •
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Employment Information Help It UK
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About the Author
iTS European are a specialist IT Recruitment agency with IT Jobs such as Desktop Support Jobs and Help Desk Support Jobs across the UK and Europe. Our recruitment professionals assist thousands of candidates to find their ideal career in the IT industry.
