I'm really having trouble with this stuff
A piece of steel will be forged into a turbine. The steel is held in a furnace at a temperature of 1250°c, and once it is taken from the furnace it can be worked until it reaches a temperature of 1100°c, after which time it will become too hard to forge successfully. Experiments have shown that the relative cooling rate for this grade of steel is about k=1.4% per minute. Suppose that the temperature of the forge shop is 30°c.
a)determine a formula for the temperature of the steel, t minutes after it is taken out of the furnace.
\(\displaystyle \L\ T-T_{s}=(T_{o}-T{s})e^{Kt}\)
\(\displaystyle \L\ T-30=(1250-30)e^{0.014t}\)
\(\displaystyle \L\ T=(1220)e^{0.014t}-30\)
b) How long can the workers forge the steel before it must be returned to the furnace for reheating?
T=1100
Ts= 30
To= 1250
K=0.014
t=?
\(\displaystyle \L\ 1100=(1220)e^{0.014t}-30\)
\(\displaystyle \L\ 1130=(1220)e^{0.014t}\)
\(\displaystyle \L\ log1130=(0.014t)log(1220)e\)
\(\displaystyle \L\ 26.05=t\)
pls help! Thanks
A piece of steel will be forged into a turbine. The steel is held in a furnace at a temperature of 1250°c, and once it is taken from the furnace it can be worked until it reaches a temperature of 1100°c, after which time it will become too hard to forge successfully. Experiments have shown that the relative cooling rate for this grade of steel is about k=1.4% per minute. Suppose that the temperature of the forge shop is 30°c.
a)determine a formula for the temperature of the steel, t minutes after it is taken out of the furnace.
\(\displaystyle \L\ T-T_{s}=(T_{o}-T{s})e^{Kt}\)
\(\displaystyle \L\ T-30=(1250-30)e^{0.014t}\)
\(\displaystyle \L\ T=(1220)e^{0.014t}-30\)
b) How long can the workers forge the steel before it must be returned to the furnace for reheating?
T=1100
Ts= 30
To= 1250
K=0.014
t=?
\(\displaystyle \L\ 1100=(1220)e^{0.014t}-30\)
\(\displaystyle \L\ 1130=(1220)e^{0.014t}\)
\(\displaystyle \L\ log1130=(0.014t)log(1220)e\)
\(\displaystyle \L\ 26.05=t\)
pls help! Thanks
