# calculus

posted by .

A cold metal bar at -30 degrees Celsius is submerged in a pool maintained at a temperature of 40 degrees Celsius. Half a minute later, the temperature of the bar is 20 degrees Celsius. How long will it take the bar to attain a temperature of 30 degrees Celsius?

I know that dy/dt=k(y-b) and y(t)=b+Ce^kt

• calculus -

The solution will be of the form

T - 40 = (-70)*exp(-kt)

Note that this satisfies T = -30 when t = 0 and T-> 40 as t -> infinity

Solve for k by using the fact that
T = 20 at t = 30 s.
-20 = -70*exp(-30 t)
exp(-30k) = 0.2857
-30k = -1.253
k = 4.18*10-2
(1/k) = 23.9 seconds

Now solve for t when T = 30 C

• Math -

I hate this
Doesn't help for me in any thing

## Similar Questions

1. ### heat

A siler bar 0.125 meter long is subjected to a temperature change from 200 degrees celsius to 100 degrees celsius what willbe the length of the bar after the temperature change?
2. ### Physical Science

Hello, I wanted to know if I came to the correct answer in the following problem... Thank You I used: I=LK(To-Tf) LD=L-I A silver bar 0.125 meter long is subjected to a temperature change from 200 degrees celsius to 100 degrees celsius. …
3. ### Math

Is this correct? The inside of your refrigerator might be set to a temperature of about____. My answer is 2.9 degrees Celsius because the choices are: A) -2.9 degrees Celsius B) 29 degrees Celsius C) 2.9 degrees Celsius D) 43.5 degrees
4. ### Chemistry

Calculate the joules of energy involved when 11 grams of water at 10.0 degrees Celsius cools and then freezes at 0.0 degrees Celsius. How many kilocalories are required to raise the temperature of 305 gtams silver from 30 degrees Celsius …
5. ### science

a silver bar 0.125 meter long is subjected to a temperature change from 2oo degrees celsius to 100 degrees Celsius what will the length of the bar be after the temperature change
6. ### Chemistry

A 50g vhuck of metal (c=0.506 j/g degrees celsius) is heated to 60 degrees celsius. It is then dropped into a calorimeter (c=1.40 j/g derees celsius, m - 5.0g) that contains 100g of liquid. The temperature of the liquid raises from …
7. ### Chemistry

A 50g chuck of metal (c=0.506 j/g degrees celsius) is heated to 60 degrees celsius. It is then dropped into a calorimeter (c=1.40 j/g derees celsius, m - 5.0g) that contains 100g of liquid. The temperature of the liquid raises from …
8. ### Physics

The water from two buckets is mixed together. One bucket contains 5kg of water at 20 degrees Celsius and the other contains 1kg of water at 80 degrees Celsius. What is the final temperature of the mixture, assuming no heat is lost …
9. ### Physics/Science

A steel bar reaches a temperature of 420 degrees celsius after it has been welded. Over the next 50 minutes the steel bar cools to 30 degrees celsius. What is the rate of temperature change of the iron?
10. ### Stats

On Tuesday September 27, 2016 the high temperature increased to 36.7 degrees Celsius (98 degrees Fahrenheit). What is the probability that we observe a temperature of 36.7 degrees Celsius or higher given that the average temperature …

More Similar Questions