A copper block is removed from a 310 C oven and dropped into 1.10 kg of water at 20.2 C. The water quickly reaches 25.4 C and then remains at that temperature.what is the mass of the block?
c1•m1 •(310-25.4) =c2•m2•(25.4-20.2)
m1= { c2•m2•(25.4-20.2)}/ c1•(310-25.4) =
={4180•1.1•5.2}/385•284.6 = 0.218 kg
To find the mass of the copper block, we can use the principle of conservation of energy. The heat gained by the water will be equal to the heat lost by the copper block.
The heat gained by the water can be calculated using the formula:
Q_water = m_water * c_water * ΔT_water
Where:
Q_water = heat gained by the water (in Joules)
m_water = mass of the water (in kg)
c_water = specific heat capacity of water (in J/kg·C)
ΔT_water = change in temperature of the water (final temperature - initial temperature) (in C)
In this case:
m_water = 1.10 kg
c_water = 4186 J/kg·C (specific heat capacity of water)
ΔT_water = (25.4 C - 20.2 C) = 5.2 C
Q_water = (1.10 kg) * (4186 J/kg·C) * (5.2 C)
Q_water ≈ 23996.32 J
According to the principle of conservation of energy, this amount of heat gained by the water is equal to the heat lost by the copper block. The heat lost by the copper block can be calculated using the formula:
Q_copper = m_copper * c_copper * ΔT_copper
Where:
Q_copper = heat lost by the copper block (in Joules)
m_copper = mass of the copper block (in kg) (what we need to find)
c_copper = specific heat capacity of copper (in J/kg·C)
ΔT_copper = change in temperature of the copper block (initial temperature - final temperature) (in C)
In this case:
c_copper = 390 J/kg·C (specific heat capacity of copper)
ΔT_copper = (310 C - 25.4 C) = 284.6 C
Now we can rearrange the formula to solve for the mass of the copper block:
m_copper = Q_copper / (c_copper * ΔT_copper)
Plugging in the values:
m_copper = (23996.32 J) / (390 J/kg·C * 284.6 C)
m_copper ≈ 2.16 kg
Therefore, the mass of the copper block is approximately 2.16 kg.
To find the mass of the copper block, we can use the principle of conservation of energy. The energy gained by the water will be equal to the energy lost by the copper block.
The equation to calculate the energy gained or lost by an object is:
Q = mcΔT
Where:
Q = heat energy gained or lost (in Joules)
m = mass of the object (in kilograms)
c = specific heat capacity of the material (in J/kg·°C)
ΔT = change in temperature (in °C)
First, let's calculate the energy gained by the water:
Qwater = mwater * cwater * ΔTwater
We know the following values:
mwater = 1.10 kg (mass of water)
cwater = 4186 J/kg·°C (specific heat capacity of water)
ΔTwater = (25.4 °C - 20.2 °C) = 5.2 °C
Substituting the values:
Qwater = (1.10 kg) * (4186 J/kg·°C) * (5.2 °C)
Qwater = 23,779.36 J
Now, since the energy gained by the water is equal to the energy lost by the copper block, we can calculate the mass of the copper block using the equation:
mcopper * ccopper * ΔTcopper = Qwater
We know the following values:
ccopper = 385 J/kg·°C (specific heat capacity of copper)
ΔTcopper = (310 °C - 25.4 °C) = 284.6 °C
Substituting the values:
(mcopper) * (385 J/kg·°C) * (284.6 °C) = 23,779.36 J
Rearranging the equation:
mcopper = 23,779.36 J / (385 J/kg·°C * 284.6 °C)
mcopper = 23,779.36 J / 109,681 J/kg
mcopper ≈ 0.217 kg
Therefore, the mass of the copper block is approximately 0.217 kg.