A 0.10 kg piece of copper at an initial temperature of 95degC is dropped into 0.20 kg of water contained in a 0.28 kg aluminum calorimeter. The water and calorimeter are initially at 15degC. What is the final temperature of the system when it reaches equilibrium?
(Cp of Copper=387J/kg * degC; Cpof Aluminum=899J/kg * degC; Cp of Water=4186J/kg * degC)
someone gave me a very long and complicated formula for this. does anyone know a simple way to solve this problem? thanks for any help
You're right. I left out a zero in the 1088.9 T term. You changed 38.7 to 39.7, but that is not a big change.
1088.92T +38.7T = 16333+3676
1127.5 T = 20,009
T = 17.7 C. Not much of an increase. That is because the heat capacity of the small piece of copper is much less than that of the calorimeter and water.
this is what i got:
0.10*387*(95-T)=0.28*899*(T-15)+0.20*4186*(T-15)
38.7(95-T)=1088.92(T-15)
1088.92T+39.7T=16333+3676
1127.62T=20009.5
and i''m confused from here
At thermal equilibrium, the heat lost by the hot copper will equal the heat gained by the water and calorimeter. By the time you have turned that fact into an equation for the final temperature, with symbols for the different masses and Cp's, you will have a lot of terms in a rather cumbersome equation. There is no other way to do it.
0.10*387*(95 - T) = 0.28*899*(T-15) + 0.20*4186*(T-15)
38.7 (95-T) = 1088.9(T-15)
188.9 T + 38.7 T = 16344 + 3676
227.6 T = 20020.
T = 88.0 C
No gurantees on the math.
To solve this problem, you can use the principle of conservation of energy.
First, calculate the amount of heat gained or lost by each component in the system.
For the copper piece, the heat gained (Q) is given by the formula Q = mass * specific heat * temperature change. Since the initial temperature is 95°C and the final temperature is unknown, you can use the formula as follows:
Q(copper) = 0.10 kg * 387 J/kg*°C * (final temperature - 95°C)
For the water, the heat gained is:
Q(water) = 0.20 kg * 4186 J/kg*°C * (final temperature - 15°C)
For the aluminum calorimeter, the heat gained is:
Q(calorimeter) = 0.28 kg * 899 J/kg*°C * (final temperature - 15°C)
According to the principle of conservation of energy, the heat gained by the copper, water, and calorimeter should equal zero when they reach equilibrium.
So, the equation becomes:
Q(copper) + Q(water) + Q(calorimeter) = 0
Simplifying and solving for the final temperature:
0.10 kg * 387 J/kg*°C * (final temperature - 95°C) + 0.20 kg * 4186 J/kg*°C * (final temperature - 15°C) + 0.28 kg * 899 J/kg*°C * (final temperature - 15°C) = 0
This equation can be rearranged and solved to find the final temperature of the system when it reaches equilibrium.
Please note that the formula may appear long and complicated due to the specific values and units involved in the calculation. However, the underlying principle is simple and relies on the conservation of energy.