i'm really lost here. please show me how to solve this
A 0.10 kg piece of copper at an initial temperature of 94 degrees C is dropped into 0.20 kg of water contained in a 0.28 kg aluminum calorimeter. The water and calorimeter are initially at 15 degrees C. What is the final temperature of the system when it reacher equilimbirum?
(Cp of Copper = 387J/kg * degC; Cp of Aluminum = 899 J/kg * degC; Cp of Water = 4186J/kg * degC)
thanks for any help
The sum of the heats gained in a closed system is zero.
masswater*cw*(Tf-Tiwater)+masscopper*Cc*(Tf-Ticopper)+massAl*Calum*(Tf-Tialum)=0
Put the numbers in, solve for Tf.
ok thanks :)
hey what is the formula for cw,Cc, and Calum plss answer it plss
To solve this problem, we need to use the principle of energy conservation. The total energy before the copper is dropped is equal to the total energy after equilibrium is reached.
Let's break down the steps to solve this problem.
Step 1: Calculate the heat transferred from the copper to the water.
We can use the equation:
Q = m * c * ΔT
where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
The heat transferred from the copper to the water is:
Q_copper = m_copper * c_copper * ΔT_copper
Using the values given, we have:
m_copper = 0.10 kg
c_copper = 387 J/(kg * °C)
ΔT_copper = T_final - T_initial, where T_initial is the initial temperature of the copper (94 °C)
Step 2: Calculate the heat transferred from the water to the calorimeter.
Similarly, we can use the equation:
Q = m * c * ΔT
The heat transferred from the water to the calorimeter is:
Q_water = m_water * c_water * ΔT_water
Using the values given, we have:
m_water = 0.20 kg
c_water = 4186 J/(kg * °C)
ΔT_water = T_final - T_initial, where T_initial is the initial temperature of the water (15 °C)
Step 3: Set up the energy conservation equation.
The total energy before the copper is dropped is equal to the total energy after equilibrium is reached. Therefore, we have:
Q_copper + Q_water = 0
Step 4: Solve the equation for the final temperature, T_final.
Substitute the values we obtained in steps 1 and 2 into the energy conservation equation and solve for T_final.
m_copper * c_copper * ΔT_copper + m_water * c_water * ΔT_water = 0
Substituting the values:
(0.10 kg) * (387 J/(kg * °C)) * (T_final - 94 °C) + (0.20 kg) * (4186 J/(kg * °C)) * (T_final - 15 °C) = 0
Now, you can solve the equation to find the value of T_final. Simplify the equation and solve for T_final.
Alternatively, you can use a numerical solver or a graphing calculator to solve this equation for T_final.
Once you have calculated T_final, you will have the final temperature of the system when it reaches equilibrium.