A technician makes a 5.0 kg metal object containing two parts£¬one of iron and the other of aluminum.If it takes 504kj to change the objects temperature from 25 celcius to 165celcius£¬what is the mass of each part£¿
heat=sum of Mal*Cal*deltaT+Mfe*Cfe*DeltaT
remember Mal+Mfe=5kg
you have two equations, two unknowns.
iron is 2 aluminum is 3
how do u do this
To determine the mass of each part (iron and aluminum) in the object, we need to solve this problem using specific heat capacity and the concept of heat transfer.
First, let's understand the formula for heat transfer:
Q = mcΔT
Where:
Q is the heat energy transferred
m is the mass of the object
c is the specific heat capacity of the substance
ΔT is the change in temperature
We have the following information:
Total mass of the object (m) = 5.0 kg
Initial temperature (T1) = 25 °C
Final temperature (T2) = 165 °C
Heat transfer (Q) = 504 kJ = 504,000 J (converting from kJ to J)
Now, let's calculate the heat transferred to the iron and aluminum parts separately:
For the iron part:
Let's assume the mass of iron as m1 kg (to be determined)
Specific heat capacity of iron (c1) = 0.45 J/g°C (or 450 J/kg°C, converting from g to kg)
Q1 = m1 x c1 x ΔT1
504,000 J = m1 x 450 J/kg°C x (165°C - 25°C)
Simplifying the equation:
504,000 J = m1 x 450 J/kg°C x 140°C
504,000 J = m1 x (450 J/kg°C) x 140°C
504,000 J = 63,000 m1 J
Divide both sides of the equation by 63,000 J to solve for m1:
m1 = 504,000 J / 63,000 J
m1 ≈ 8 kg
For the aluminum part:
Since we know the total mass of the object (5.0 kg) and the mass of the iron part (8 kg), we can find the mass of the aluminum part:
m2 = Total mass - Mass of iron
m2 = 5.0 kg - 8 kg
m2 = -3.0 kg
However, it is not logical for the mass of the aluminum part to be negative. This indicates an error in the calculation or the given information. Please double-check the values provided or the problem statement.