exactly 60.0g of cold solid copper was placed in 45.0g of water, the water temperature decreases from 20.0*c to 18.5*c. calculate the initial temprature of the copper
To solve this problem, we can use the equation:
q = mcΔT
where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's calculate the heat transferred from the copper:
q_copper = mcΔT
= (60.0g)(c_copper)(T_initial - 18.5°C)
Second, let's calculate the heat transferred from the water:
q_water = mcΔT
= (45.0g)(c_water)(20.0°C - 18.5°C)
= (45.0g)(4.18 J/g°C)(1.5°C)
= 282.15 J
Since the heat transferred from the copper and the water are equal (according to the conservation of energy), we can set up the equation:
q_copper = q_water
(60.0g)(c_copper)(T_initial - 18.5°C) = 282.15 J
Now, we can solve for T_initial:
T_initial - 18.5°C = 282.15 J / ((60.0g)(c_copper))
T_initial = (282.15 J / ((60.0g)(c_copper))) + 18.5°C
Note: The specific heat capacity of copper is 0.385 J/g°C, so you would need to substitute the appropriate value for c_copper in the equation above.
To calculate the initial temperature (T1) of the copper, we can use the principle of energy conservation. The heat lost by the copper (Qc) is equal to the heat gained by the water (Qw):
Qc = Qw
We can calculate the heat lost by the copper using the formula:
Qc = mc * cc * (T1 - T2)
where mc is the mass of the copper, cc is the specific heat capacity of copper, and T2 is the final temperature of the copper.
We can calculate the heat gained by the water using the formula:
Qw = mw * cw * (T2 - T1)
where mw is the mass of the water, cw is the specific heat capacity of water, and T2 - T1 is the temperature change of the water.
Since we know the masses of the copper and water, the specific heat capacities of copper and water, and the final temperature (T2) of both the copper and water, we can rearrange the heat equations to solve for the initial temperature (T1) of the copper.
Using the given values:
mc = 60.0 g
cc = 0.387 J/g°C (specific heat capacity of copper)
mw = 45.0 g
cw = 4.18 J/g°C (specific heat capacity of water)
T2 (final temperature) = 18.5°C
T2 - T1 (temperature change of water) = 20.0°C - 18.5°C = 1.5°C
Substituting these values into the equations, we get:
Qc = mc * cc * (T1 - T2)
Qw = mw * cw * (T2 - T1)
Since Qc = Qw, we can set the equations equal to each other and solve for T1:
mc * cc * (T1 - T2) = mw * cw * (T2 - T1)
Simplifying the equation:
60.0 g * 0.387 J/g°C * (T1 - 18.5°C) = 45.0 g * 4.18 J/g°C * (18.5°C - T1)
Now we can solve for T1 by isolating it:
60.0 g * 0.387 J/g°C * T1 - 60.0 g * 0.387 J/g°C * 18.5°C = 45.0 g * 4.18 J/g°C * 18.5°C - 45.0 g * 4.18 J/g°C * T1
Multiply the terms:
23.22 g * T1 - 1126.2 g°C = 378.45 g * °C - 187.11 g * T1
Combine like terms:
23.22 g * T1 + 187.11 g * T1 = 378.45 g * °C + 1126.2 g°C
Combine the constants:
210.33 g * T1 = 1504.65 g°C
Divide both sides by 210.33 g:
T1 = 1504.65 g°C / 210.33 g
T1 = 7.15°C
Therefore, the initial temperature (T1) of the copper is approximately 7.15°C.
To solve this problem, we can use the principle of conservation of heat, which states that the heat released by the copper when it cools down is equal to the heat absorbed by the water when it warms up. Mathematically, we can express this as:
Heat released by copper = Heat absorbed by water
The heat released by the copper is given by the formula:
Q = m * c * ΔT
Where:
Q = heat released (or absorbed), which can be positive or negative
m = mass of the substance (copper in this case)
c = specific heat capacity of the substance (copper in this case)
ΔT = change in temperature (final temperature - initial temperature)
For copper, the specific heat capacity (c) is approximately 0.386 J/g°C.
Given:
Mass of copper (m) = 60.0 g
Initial temperature of water = 20.0 °C
Final temperature of water = 18.5 °C
Mass of water = 45.0 g
We can calculate the heat released by copper using the formula:
Q_copper = m_copper * c_copper * ΔT_copper
Where:
m_copper = mass of copper = 60.0 g
c_copper = specific heat capacity of copper = 0.386 J/g°C
ΔT_copper = change in temperature of copper = final temperature of copper - initial temperature of copper
Q_water = m_water * c_water * ΔT_water
Where:
m_water = mass of water = 45.0 g
c_water = specific heat capacity of water = 4.18 J/g°C
ΔT_water = change in temperature of water = final temperature of water - initial temperature of water
According to the principle of conservation of heat:
Q_copper = -Q_water (Note that the negative sign indicates that the heat is transferred from copper to water)
By substituting the given values into the equations and solving for the unknown initial temperature of copper, we can find the answer.