a metal is heated up to a temperature

Mark Parayno

Mark Parayno

Answered question

2022-08-03

a metal is heated up to a temperature of 500 degree celsius. it is then exposed to a temperature of 38 degree celsius. after 2 minutes the temperature of the metal becomes 190 degree celsius when will the temperature be 100 degree celsius. what is the temperature after 4 minutes

Answer & Explanation

alenahelenash

alenahelenash

Expert2023-06-19Added 556 answers

To solve this problem, let's analyze the given information.
We have:
- Initial temperature of the metal: T0=500C
- Temperature at which the metal is exposed: Te=38C
- Temperature of the metal after 2 minutes: T2=190C
Part A: When will the temperature be 100 degrees Celsius?
To find the time at which the temperature of the metal will be 100 degrees Celsius, we can assume that the rate of temperature change is constant. Therefore, we can set up a proportion:
T2TeTTe=t2t
Where:
- T is the temperature we want to find (in this case, T=100C)
- t is the time we want to find
- T2 is the temperature after 2 minutes
- t2 is the given time (2 minutes)
Substituting the known values, we have:
190C38C100C38C=2mint
Simplifying the equation, we get:
15262=2t
Cross-multiplying, we have:
152·t=62·2
Solving for t, we find:
t=62·2152
t0.816min
Therefore, the temperature of the metal will be 100 degrees Celsius approximately 0.816 minutes after it reaches a temperature of 190 degrees Celsius.
Part B: What is the temperature after 4 minutes?
To find the temperature of the metal after 4 minutes, we can again assume that the rate of temperature change is constant. Using the same proportion as before, we have:
T2TeTTe=t2t
Substituting the known values:
190C38CT38C=2min4min
Simplifying the equation:
152T38=12
Cross-multiplying:
2·(T38)=152
2T76=152
2T=228
T=114C
Therefore, the temperature of the metal after 4 minutes is 114 degrees Celsius.
The solutions are represented as:
Part A: t0.816min
Part B: T=114C

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