A copper pot with mass 0.5 Kg contains 0.17 kg of water at a temperature of 20
degree celcius . A 0.8 kg hot solid having specific heat capacity 390 J/KgK at 80
degree celcius is dropped into the pot. Find the final temperature of mixture. (Sp.
Heat capacity of copper = 400 J/KgK and water = 4200 J/KgK)
[mass pot x specific heat pot x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [mass solid x specific heat solid x (Tfinal-Tinitial)] = 0
Substitute and solve for Tfinal. Tfinal is the only unknown in the above equation. Post your work if you get stuck.
To find the final temperature of the mixture, we can use the principle of conservation of energy.
First, let's calculate the energy gained or lost by each component:
1. Copper Pot:
The heat gained or lost by the copper pot can be calculated using the formula Q = mcΔT, where Q is the heat change, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The initial temperature of the copper pot is 20 degrees Celsius, and we want to find the final temperature. Therefore, ΔT = Tf - Ti.
Substituting the values, we have Qcopper = mcopper * ccopper * (Tf - 20).
2. Water:
The heat gained or lost by the water can be calculated using the same formula: Q = mcΔT.
The initial temperature of the water is also 20 degrees Celsius.
Substituting the values, we have Qwater = mwater * cwater * (Tf - 20).
3. Hot Solid:
The heat gained or lost by the hot solid can also be calculated using the same formula: Q = mcΔT.
The initial temperature of the hot solid is 80 degrees Celsius.
Substituting the values, we have Qsolid = msolid * csolid * (Tf - 80).
According to the principle of conservation of energy, the total energy gained by the water, copper pot, and hot solid is equal to the energy lost by the hot solid.
Therefore, Qcopper + Qwater + Qsolid = 0.
Now, let's calculate the final temperature (Tf) using the given values:
Qcopper = mcopper * ccopper * (Tf - 20)
Qwater = mwater * cwater * (Tf - 20)
Qsolid = msolid * csolid * (Tf - 80)
Substituting the values:
0.5 * 400 * (Tf - 20) + 0.17 * 4200 * (Tf - 20) + 0.8 * 390 * (Tf - 80) = 0
This equation can be solved to find the final temperature of the mixture.
To find the final temperature of the mixture, we need to use the principle of energy conservation.
First, let's calculate the heat exchanged between the solid and the pot, as well as between the water and the pot:
1. The heat exchanged between the solid and the pot can be calculated using the specific heat capacity formula:
Q1 = m1 * c1 * (Tf - Ti)
where
- Q1 is the heat exchanged
- m1 is the mass of the solid
- c1 is the specific heat capacity of the solid
- Tf is the final temperature of the mixture
- Ti is the initial temperature of the solid
Plugging in the values, we have:
Q1 = 0.8 kg * 390 J/kgK * (Tf - 80°C)
2. The heat exchanged between the water and the pot can also be calculated using the specific heat capacity formula:
Q2 = m2 * c2 * (Tf - Ti)
where
- Q2 is the heat exchanged
- m2 is the mass of the water
- c2 is the specific heat capacity of water
- Tf is the final temperature of the mixture
- Ti is the initial temperature of the water
Plugging in the values, we have:
Q2 = 0.17 kg * 4200 J/kgK * (Tf - 20°C)
According to the principle of energy conservation, the heat exchanged between the solid and the pot must be equal to the heat exchanged between the water and the pot. Therefore, we can set up an equation with Q1 and Q2:
Q1 = Q2
0.8 kg * 390 J/kgK * (Tf - 80°C) = 0.17 kg * 4200 J/kgK * (Tf - 20°C)
Now, let's solve for Tf:
0.8 * 390 * (Tf - 80) = 0.17 * 4200 * (Tf - 20)
312 * (Tf - 80) = 714 * (Tf - 20)
312Tf - 24960 = 714Tf - 14280
714Tf - 312Tf = -14280 + 24960
402Tf = 10680
Tf = 10680 / 402
Tf ≈ 26.57°C
Therefore, the final temperature of the mixture is approximately 26.57 degrees Celsius.