A metal container, which has a mass of 9.4 kg contains 14.2 kg of water. A 1.7-kg piece of the same metal, initially at a temperature of 160.0°C, is dropped into the water. The container and the water initially have a temperature of 15.0°C and the final temperature of the entire system is 17.0°C. Calculate the specific heat of the metal.
I got 124.73 but when I put units in it says it's wrong. What are the units? Please help. Units always confuse me.
ΔQ1 + ΔQ2 = ΔQ3,
c• m1•ΔT1 +ñ(w) •m2• ΔT1 = c• m3•ΔT2,
ñ(w) •m2• ΔT1 = c• (m3•ΔT2 - m1•ΔT1),
c = {ñ(w) •m2• ΔT1}/{m3•ΔT2 - m1•ΔT1} =
=4180•14.2•2/(143•1.7 – 9.4•2) = 530.5 J.
Expiain why a piece of wood floats in water?
To calculate the specific heat of the metal, you need to use the formula:
Q = mcΔT
Where:
Q is the heat absorbed or released by the metal (in joules)
m is the mass of the metal (in kg)
c is the specific heat capacity of the metal (in J/kg°C)
ΔT is the change in temperature of the metal (in °C)
First, we need to find the heat absorbed by the water:
Q_water = mc_waterΔT_water
Where:
m_water is the mass of the water (in kg)
c_water is the specific heat capacity of water (about 4186 J/kg°C, rounded to the nearest whole number)
ΔT_water is the change in temperature of the water (final temperature - initial temperature)
Q_water = (14.2 kg) * (4186 J/kg°C) * (17.0°C - 15.0°C)
Q_water = 14.2 kg * 4186 J/kg°C * 2.0°C
Q_water = 59,068.8 J
Next, we need to find the heat absorbed by the container:
Q_container = mc_containerΔT_container
Where:
m_container is the mass of the container (in kg)
c_container is the specific heat capacity of the container (which we need to find)
ΔT_container is the change in temperature of the container (final temperature - initial temperature)
We can set up an equation to solve for c_container:
Q_container = mc_containerΔT_container
Q_container = (9.4 kg) * c_container * (17.0°C - 15.0°C)
Q_container = (18.8 kg°C) * c_container
Since the final temperature of the system is 17.0°C, the container did not experience any temperature change (ΔT_container = 0), so Q_container = 0.
Therefore, the heat absorbed or released by the metal is equal to the total heat absorbed by the system:
Q_metal = Q_water + Q_container
Q_metal = 59,068.8 J
Finally, we can solve for the specific heat of the metal:
Q_metal = mc_metalΔT_metal
mc_metalΔT_metal = 59,068.8 J
Now, let's substitute the given values into the equation:
(1.7 kg) * c_metal * (17.0°C - 160.0°C) = 59,068.8 J
(1.7 kg) * c_metal * (-143.0°C) = 59,068.8 J
c_metal = 59,068.8 J / (1.7 kg * -143.0°C)
Now, let's calculate the specific heat of the metal:
c_metal = -235.5 J/kg°C
The specific heat of the metal is approximately -235.5 J/kg°C.
Note: In the calculation, the units cancel out, leaving the remaining units as specific heat capacity in J/kg°C.
To calculate the specific heat of the metal, we can use the equation:
Q = m * c * ΔT,
where:
- Q is the heat transferred,
- m is the mass of the substance (in this case, the metal),
- c is the specific heat of the substance, and
- ΔT is the change in temperature.
Since the metal and the container are made of the same material, we can consider them as a single entity. Let's calculate the heat transferred between the metal and the water using this equation:
Q₁ = m₁ * c₁ * ΔT,
where:
- Q₁ is the heat transferred between the metal and the water,
- m₁ is the mass of the metal,
- c₁ is the specific heat of the metal, and
- ΔT is the change in temperature.
We know that the final temperature of the system is 17.0°C. Therefore, the change in temperature for both the metal and the water is:
ΔT = final temperature - initial temperature = 17.0°C - 15.0°C = 2.0°C.
According to the problem statement, the mass of the metal is 1.7 kg. So, we have:
Q₁ = 1.7 kg * c₁ * 2.0°C.
We also know that the water in the container initially had a mass of 14.2 kg and its specific heat is approximately 4.18 J/g°C.
Now, let's calculate the heat transferred between the water and the metal:
Q₂ = m₂ * c₂ * ΔT,
where:
- Q₂ is the heat transferred between the water and the metal,
- m₂ is the mass of the water (14.2 kg),
- c₂ is the specific heat of water (4.18 J/g°C),
- ΔT is the change in temperature (2.0°C).
Converting the mass of the water from kg to grams:
m₂ = 14.2 kg * 1000 g/kg = 14200 g.
Now, let's calculate the heat transferred between the water and the metal:
Q₂ = 14200 g * 4.18 J/g°C * 2.0°C.
The total heat transferred in the system is equal to the sum of Q₁ and Q₂, because energy is conserved:
Q = Q₁ + Q₂.
Given that the initial temperature of the metal is 160.0°C, we can rearrange the equation to solve for c₁:
Q₁ = m₁ * c₁ * ΔT,
c₁ = Q₁ / (m₁ * ΔT).
Once you calculate the values for Q₁, Q₂, and Q, divide Q₁ by (m₁ * ΔT) to get the specific heat of the metal. Be sure to use consistent units throughout your calculations, such as grams for mass and Joules (J) for energy. Let's calculate the specific heat of the metal using the provided data and equations.