Ftension

Newton's law of cooling is , where is the temperature of an object, is in hours, is a constant ambient temperature, and is a pos

kirill [66]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The time taken is $t = 6.89 \ hrs$

Explanation:

From the question we are told that

The value of $k = 0.15hr^{-1}$

The the interior temperature is $u(t = 0) = 70 ^oF$

The external temperature is $T = 11 ^oF$

The required interior temperature is $u_{t} = 32 ^oF$

The newton cooling law is

$\frac{du}{dt} = -k (u -T)$

=> $\frac{du}{u-T} = - kdt$

Now integrate both sides we have

$\int\limits \frac{du}{u-T} =\int\limits - kdt$

$ln (u - T) = -kt + c$

Since c is a constant lnC = c will also give a constant so

$ln (u - T) = -kt + ln C$

=> $\frac{(u -T)}{C} = e^{-kt}$

=> $u = T + Ce^{-kt}$

substituting value

$70 = 11 +Ce^{-0* 0.15}$

$C = 59$

Hence

$u_t = 11 + 59 e^{-0.15 *t}$

$32= 11 + 59 e^{-0.15 *t}$

=> $t = -\frac{ln(\frac{21}{59} )}{0.15}$

$t = 6.89 \ hrs$

3 0

2 years ago

The power of a bulb is 100 watt .what does it mean

natita [175]

Answer:

Explanation: 100 watts is a unit of power.

A watt is also the amount of energy being consumed. So the more watts the brighter the light bulb is lit.

3 0

2 years ago

If Earth were 10.0 times farther away from the Sun than it is now, how many times weaker would the gravitational force between t

choli [55]

If Earth were 10.0 times farther away from the Sun than it is now, 100 times weaker would the gravitational force between the Sun and Earth.

What is Gravitational Force?

According to Newton's universal law of gravitation, The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them.

What causes gravitational force?

Earth's gravity comes from all its mass. All its mass makes a combined gravitational pull on all the mass in your body. That's what gives you weight. And if you were on a planet with less mass than Earth, you would weigh less than you do here.

Learn more about gravitational force:

brainly.com/question/862529

#SPJ4

5 0

1 year ago

WHICH ROLLER COASTER CART HAS THE LEAST POTENTIAL ENERGY DUE TO GRAVITY?

DIA [1.3K]

Answer:

C. Car A

Explanation:

if the answer is: which roller coaster car has the greatest potential energy due to gravity brainly

6 0