1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
VikaD [51]
3 years ago
6

A thermometer having first-order dynamics with a time constant of 1 min is placed in a temperature bath at 100oF. After the ther

mometer reaches steady state, it is suddenly placed in a bath at 110oF at t = 0 and left there for 1 min, after which it is immediately returned to the bath at 100oF.(a) Plot the variation of the thermometer reading with time (No hand-sketched plot please).(b) Calculate the thermometer reading at t = 0.5 min and at t = 2.0 min.

Chemistry
1 answer:
sveticcg [70]3 years ago
6 0

Answer:

(a) See below

(b) 103.935 °F; 102.235 °F

Explanation:

The equation relating the temperature to time is

T = T_{0} + \Delta T\left (1 - e^{-t/\tau} \right )

1. Calculate the thermometer readings after  0.5 min and 1 min

(a) After 0.5 min

\begin{array}{rcl}T & = & T_{0} + \Delta T\left (1 - e^{-t/\tau} \right )\\ & = & 100 + 10\left (1 - e^{-0.5/1} \right )\\ & = & 100 + 10\left (1 - e^{-0.5} \right )\\ & = & 100 + 10 (1 - 0.6065)\\ & = & 100 + 10(0.3935)\\ & = & 100 + 3.935\\ & = & 103.935\,^{\circ}F\\\end{array}

(b) After 1 min

\begin{array}{rcl}T & = & T_{0} + \Delta T\left (1 - e^{-t/\tau} \right )\\ & = & 100 + 10\left (1 - e^{-1/1} \right )\\ & = & 100 + 10\left (1 - e^{-1} \right )\\ & = & 100 + 10 (1 - 0.3679)\\ & = & 100 + 10(0.6321)\\ & = & 100 + 6.321\\ & = & 106.321\,^{\circ}F\\\end{array}

2. Calculate the thermometer reading after 2.0 min

T₀ =106.321 °F

ΔT = 100 - 106.321 °F = -6.321 °F

  t = t - 1, because the cooling starts 1 min late

\begin{array}{rcl}T & = & T_{0} + \Delta T\left (1 - e^{-(t - 1)/\tau} \right )\\ & = & 106.321 - 6.321\left (1 - e^{-(2 - 1)/1} \right )\\ & = & 106.321 - 6.321\left (1 - e^{-1} \right )\\ & = & 106.321 - 6.321 (1 - 0.3679)\\ & = & 106.321 - 6.321 (0.6321)\\ & = & 106.321 - 3.996\\ & = & 102.325\,^{\circ}F\\\end{array}

3. Plot the temperature readings as a function of time.

The graphs are shown below.

You might be interested in
Which of the following equations is correct for coffee-cup calorimeter?
Bogdan [553]

The equation that is correct for coffee-cup calorimeter is q reaction = -q calorimeter. Details about coffee-cup calorimeter.

<h3>What is a calorimeter?</h3>

A calorimeter is an apparatus for measuring the heat generated or absorbed by either a chemical reaction, change of phase or some other physical change.

A coffee-cup calorimeter is a specific type of calorimeter that involves the absorption of heat of a reaction by water when a reaction occurs.

The enthalpy change of the reaction is equal in magnitude but opposite in sign to the heat flow for the water:

qreaction = -(qwater)

Therefore, the equation that is correct for coffee-cup calorimeter is q reaction = -q calorimeter.

Learn more about coffee-cup calorimeter at: brainly.com/question/27828855

#SPJ1

3 0
1 year ago
How much pure acid is in 520 milliliters of a 13 ​% ​solution?
Liono4ka [1.6K]
It actually depends on the percentage of the concentration give. Percentages can be expressed as %mass/mass, %volume/volume or %mass/volume. To keep things simple, let's just assume that it is in %volume/volume. Thus, 13% of 520 mL is pure acid.

Volume of pure acid = 520*0.13 = 67.6 mL
4 0
3 years ago
The smallest unit of a compound is called a ___________.
Oxana [17]
<span>The smallest unit of a compound is called a molecule. The correct option among all the options that are given in the question is the second option or the penultimate option or option "B". The other choices are incorrrect and can be negated. I hope that this is the answer that has actually come to your desired help.</span>
5 0
3 years ago
What is the difference between alkali metals and halogens?
Airida [17]
<h3>→soft and reactive metals. </h3>

Explanation:

<h3>Alkali metals are soft and reactive metals. They react vigorously with water and become more reactive. And other hand halogens are reactive non metals. ... Halogens can be solid, liquid, gaseous at room temperature and the melting point increase when they get bigger.</h3>

<h2>#CAREYINGTOLEARN❤️</h2>
4 0
2 years ago
Read 2 more answers
Many grasses and few trees characterize ____________ (tundras/temperate grasslands).
Oksanka [162]

Answer:

Temperate Grasslands

Explanation:

Tundras have nothing to do with grass. Tundras are more like ice

8 0
3 years ago
Read 2 more answers
Other questions:
  • What describes redshift
    5·1 answer
  • The temperature of a 500. ml sample of gas increases from 150. k to 350. k. what is the final volume of the sample of gas, if th
    11·2 answers
  • For the reaction A (g) → 3 B (g), Kp = 80100 at 298 K. When ∆G = -14.2 kJ/mol, what is the partial pressure of A when the partia
    13·1 answer
  • A 40.2 g sample of a metal heated to 99.3°C is placed into a calorimeter containing 120 g of water at 21.8°C. The final temper
    8·1 answer
  • Express 749 000 000 in scientific notation,
    13·1 answer
  • How many atoms of hydrogen combine with one carbon atom to form methane
    14·1 answer
  • What is the valence number of an element that has 3 electron in its outermost shell?
    15·1 answer
  • Los materiales sinteticos tienen implicaciones en el medio ambiente​
    15·1 answer
  • Chase buys a helium balloon for a friend's birthday. As he walks out of the store, it starts snowing.
    12·1 answer
  • PLEASE HELP!! WILL MARK BRAINLIEST
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!