Question

The temperature of your coffee is 50°C at t=0. How long will it take for the temperature to reach 35°C if the rate of heat loss from the surface is constant at 2500 W/m²? Assume the cup has a diameter of 10 cm and a height of 20 cm. The Area of the cup is $\pi \times radius^2$. Assume the bottom and side walls are well-insulated (no heat transfer). Density is 1000 kg/m³ and $c_p$ is 4.186 J/g/°C.

          The temperature of your coffee is 50°C at t=0. How long will it take for the temperature to reach 35°C if the rate of heat loss from the surface is constant at 2500 W/m²? Assume the cup has a diameter of 10 cm and a height of 20 cm. The Area of the cup is $\pi \times radius^2$. Assume the bottom and side walls are well-insulated (no heat transfer). Density is 1000 kg/m³ and $c_p$ is 4.186 J/g/°C.
        
Show more…
The temperature of your coffee is 50°C at t=0. How long will it take for the temperature to reach 35°C if the rate of heat loss from the surface is constant at 2500 W/m²? Assume the cup has a diameter of 10 cm and a height of 20 cm. The Area of the cup is π× radius^2. Assume the bottom and side walls are well-insulated (no heat transfer). Density is 1000 kg/m³ and cp is 4.186 J/g/°C.

Added by Adrian C.

Close

Chemistry: Structure and Properties
Chemistry: Structure and Properties
Nivaldo Tro 2nd Edition
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
The temperature of your coffee is 50°C at t=0. How long will it take for the temperature to reach 35°C if the rate of heat loss from the surface is constant at 2500 W/m^2? Assume the cup has a diameter of 10 cm and a height of 20 cm. The area of the cup is π * radius^2. Assume the bottom and side walls are well-insulated (no heat transfer). Density is 1000 kg/m^3 and cp is 4.186 J/g/°C.
Close icon
Play audio
Feedback
Powered by NumerAI
Danielle Fairburn David Collins
Kathleen Carty verified

Adi S and 80 other subject Chemistry 101 educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
as-a-coffee-enthusiast-you-wish-to-keep-your-coffee-as-hot-as-possible-for-as-long-as-possible-you-wish-to-find-the-rate-of-heat-loss-of-a-typical-coffee-mug-assume-the-mug-to-be-a-cylinder-75472

As a coffee enthusiast you wish to keep your coffee as hot as possible for as long as possible. You wish to find the rate of heat loss of a typical coffee mug. Assume the mug to be a cylinder which has a lid made out of the same material as the rest of the cylinder, and the thickness of the walls is 1.17 cm. If the coffee in the mug is 77.1 °C and the room temperature is 24.0 °C how much more heat does the mug lose through conduction than from radiated energy.

Adi S.

the-temperature-of-cup-of-coffee-is-determined-by-newtons-law-of-cooling-tt-poekt-c-suppose-the-room-temperature-is-70-degrees-f_-and-the-cup-of-coffee-starts-out-at-180-degrees-at-t-0-if-th-89535

The temperature of a cup of coffee is determined by Newton's Law of Cooling: T(t) = P0e^kt + C. Suppose the room temperature is 70 degrees F, and the cup of coffee starts out at 180 degrees at t = 0. If the cooling rate is k = -.0489, determine how long it will take for the coffee to cool to 100 degrees.

Adi S.

a-cup-of-coffee-is-poured-from-a-pot-whose-contents-are-95c-into-a-non-insulated-cup-in-a-room-at-209-after-a-minute-the-coffee-has-cooled-t0-90c-how-much-time-is-required-before-the-coffee-34192

A cup of coffee is poured from a pot whose contents are 95°C into a non-insulated cup in a room at 20°C. After a minute, the coffee has cooled to 90°C. How much time is required before the coffee reaches a drinkable temperature of 65°C?

Alec T.


*

Recommended Textbooks

-
Chemistry: Structure and Properties

Chemistry: Structure and Properties

Nivaldo Tro 2nd Edition
achievement 1,914 solutions
Chemistry The Central Science

Chemistry The Central Science

Theodore L. Brown 14th Edition
achievement 1,207 solutions
Chemistry

Chemistry

Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste 10th Edition
achievement 1,625 solutions

*

Transcript

-
00:01 See here d is given that is 5 centimeter so this will be equal to 0 .05 meter and t1 is given that is 95 degree okay and temperature t2 is given 21 degree celsius and k is given that is 8 .36 times 10 to the power minus 2 okay and a will be equal to 6 a…
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever