Physics, 16.07.2019 02:30 bthomas78

The differential equation below models the temperature of a 91°c cup of coffee in a 21°c room, where it is known that the coffee cools at a rate of 1°c per minute when its temperature is 71°c. solve the differential equation to find an expression for the temperature of the coffee at time t. (let y be the temperature of the cup of coffee in °c, and let t be the time in minutes, with t = 0 corresponding to the time when the temperature was 91°c.) dy/dt =(− 1/50)(y − 21)

Answers: 1

Show answers

Answers

Answer from: hiiliohi1018

$T=21+70e^{\frac{-t}{50} }$

Explanation:

We start from:

$\frac{dT}{dt}=\frac{-1}{50}(T-21)$

Separating variables:

-50dT=(T-21)dt

$-50\frac{dT}{T-21}=dt$

Integrating with initial conditions:

$-50\int\limits^{T}_{91} {\frac{1}{T-21} } \, dT= \int\limits^t_{0} {} \, dt$

$-50ln(\frac{T-21}{91-21})=t$

$ln(\frac{T-21}{71})=\frac{-t}{50}$

Isolating T:

$\frac{T-21}{70} =e^\frac{-t}{50} }$

$T=21+70e^{\frac{-t}{50} }$

You may note that when t is zero the temperature is 91 ºC, as is specified by the problem. As well, when t is bigger (close to infinite), the temperature tends to be the room temperature (21 ºC)

Answer from: Quest

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this

Answer from: Quest

Your answer would be, the due process clause of the 14th., and 5th. amendments differ the clause in the 14th. amendment has been interpreted, to mean that state government must provide some of the protections within the bill of rights.your answer would be, the clause in the 5th. amendment was specifically written to restrict a new powerful government.hope that !