The temperature of piece of copper of mass 250g is raised to 100% and is then transferred to well lagged aluminum can mass 10g containing 120g of methylated spirit at 10%.
Calculate the final steady temperature after the spirit has been well stirred. Neglect the heat capacity of the
C for copper= 400j/kg/k
C2 methylated spirit = 2400j/kg/k
C for alluminium = 900j/kg
It is a problem to me
To calculate the final steady temperature after the spirit has been well stirred, we need to use the principle of energy conservation.
The equation we can use is:
Q1 + Q2 = 0
where Q1 is the heat gained by the copper and Q2 is the heat lost by the methylated spirit.
First, let's calculate Q1, the heat gained by the copper:
Q1 = m1 * C1 * ΔT1
where m1 is the mass of the copper, C1 is the specific heat capacity of copper, and ΔT1 is the change in temperature for the copper.
m1 = 250g
C1 = 400 J/kg/K
ΔT1 = 100% = 100K
Plugging in the values:
Q1 = (250g) * (400 J/kg/K) * (100K) = 10,000 J
Next, let's calculate Q2, the heat lost by the methylated spirit:
Q2 = m2 * C2 * ΔT2
where m2 is the mass of the methylated spirit, C2 is the specific heat capacity of methylated spirit, and ΔT2 is the change in temperature for the methylated spirit.
m2 = 120g
C2 = 2400 J/kg/K
ΔT2 = ΔT1 (since the final temperature is the same)
Plugging in the values:
Q2 = (120g) * (2400 J/kg/K) * (100K) = 2,880,000 J
Next, let's calculate the change in temperature for the methylated spirit:
ΔT2 = Q2 / (m2 * C2)
Plugging in the values:
ΔT2 = (2,880,000 J) / ((120g) * (2400 J/kg/K)) = 10K
Now, since the final temperature is the same for both the copper and the methylated spirit:
Final temperature = Initial temperature of the copper + ΔT2
The initial temperature of the copper is not given in the problem statement. You would need to provide the initial temperature of the copper to get the final steady temperature after the spirit has been stirred.
Hope this helps!