a 200g aluminum container has 500g of water with an initial temperature of 22 degree celsius. The following heated pieces of metal are dropped into water at the same time as follows: 300g piece of aluminum heated at 100 degree celsius; a 50g piece of copper heated at 80 degree celsius and a 40g piece of steel heated at 120 degree celsius. What will be the final temperature of the mixture?
Al: m1= 0,2 kg, t1= 22 ºC, c1 = 897 J/kg•ºC
Water: m2= 0.5 kg, t1= 22 ºC, c2= 4180 J/kg•ºC
Al: m3= 0.3 kg, t3= 100 ºC, c1=897 J/kg•ºC
Cu: m4=0.05 kg, t4=80 ºC, c4=385 J/kg•ºC
Steel: m5 =0.04 kg, t5=120 ºC, c5=466 J/kg•ºC
m1•c1•(t-t1) + m2•c2• (t-t1) =m3•c1• (t3-t)+m4•c4• (t4-t)+m5•c5v(t5-t).
Solve for „t“
Use the specific heat of metal formula for each metal to compute for the Tmix. Then, sum all the Tmix to get the Total Tmix.
OK ooooo
It is ok
To find the final temperature of the mixture, we need to use the principle of heat transfer.
The heat gained or lost by an object can be calculated using the formula:
Q = m * c * ΔT
where Q is the heat transferred, m is the mass of the object, c is the specific heat capacity of the material, and ΔT is the change in temperature.
First, let's calculate the heat gained or lost by the aluminum container:
Q_aluminum = m_aluminum * c_aluminum * (T_final - T_initial)
= 200g * c_aluminum * (T_final - 22°C)
Next, let's calculate the heat gained or lost by the water:
Q_water = m_water * c_water * (T_final - T_initial)
= 500g * c_water * (T_final - 22°C)
The total heat gained by the system is equal to the sum of the heat gained by the aluminum, copper, and steel pieces:
Q_total = Q_aluminum + Q_copper + Q_steel
Since the total heat gained by the system is zero (assuming no heat is lost to the surroundings), we can set Q_total equal to zero and solve for the final temperature (T_final).
Q_aluminum + Q_copper + Q_steel = 0
Plugging in the values:
200g * c_aluminum * (T_final - 22°C) +
50g * c_copper * (T_final - 80°C) +
40g * c_steel * (T_final - 120°C) = 0
Simplifying the equation and solving for T_final will give us the final temperature of the mixture.