A metal is heated up to a temperature of 500^{\circ}C.

Stefan Hendricks

Stefan Hendricks

Answered question

2021-12-29

A metal is heated up to a temperature of 500C. It is then exposed to a temperature of 38C. After 2 minutes, the temperature of the metal becomes 190C. When will the temperature be 100C?

Answer & Explanation

puhnut1m

puhnut1m

Beginner2021-12-30Added 33 answers

Initial temp =500C
Ta=Ambient temp=38C
After 2 min, temp =190C
Calculate: Time when temp reaches to 100C
dTdt=K(TTa)
dTTTa=K dt
500190dTTTa=K02dt
t=0,T=500C
t=2,T=190C
[ln(TTa)]500190=K(20)
ln23176=2Kk=12ln23176
dTTTa=Kdt
t=0,T=500C
T=t,T=100C
500100dTTTa=k0tdt
[ln(TTa)]500100=k(t0)
ln(10038)ln(50038)=kt
ln(1003850038)=12ln(23176)t
Answer: t=3.61 minute
Neunassauk8

Neunassauk8

Beginner2021-12-31Added 30 answers

The mean temperature of the metal as it cools from 500C to 190C is,
θ=500+1902
θ=6902=345C
The rate of decrease of temperature is,
5001902=155 deg Cmin
According to the Newtons
karton

karton

Expert2022-01-09Added 613 answers

Ta=Ambient temp=38C=190C100CdTdt=K(TTa)dTTTa=K dt500190dTTTa=K02dtt=0,T=500Ct=2,T=190C[ln(TTa)]500190=K(20)ln23176=2Kk=12ln23176dTTTa=Kdtt=0,T=500CT=t,T=100C500100dTTTa=k0tdt[ln(TTa)]500100=k(t0)ln(10038)ln(50038)=ktln(1003850038)=12ln(23176)tAnswer: t=3.61 minute

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