A hot iron ball is dropped into 200g of cooler water. The water temperature increases by 2.0 degrees C and the temperature of the ball decreases by18.6 degrees C. What is the mass of the iron ball?
Q1=Q2
c(i) •m(i) •ΔT(i) = c(w) •m(w) •ΔT(w)
444• m•18.6=4180•0.2•2
m=4180•0.2•2/444•18.6 =0.2 kg
To solve this problem, we can use the principle of conservation of energy. The energy lost by the iron ball is equal to the energy gained by the water.
First, let's calculate the energy gained by the water:
Q = mcΔT
Where:
Q is the energy gained
m is the mass of the water
c is the specific heat capacity of water (4.184 J/g°C)
ΔT is the change in temperature
Given:
m (water) = 200g
ΔT (water) = 2.0°C
c (water) = 4.184 J/g°C
Plugging in the values:
Q = (200g) * (4.184 J/g°C) * (2.0°C)
Q = 1673.6 J
Now, let's calculate the energy lost by the iron ball:
Q = mcΔT
Again, Q represents the energy lost, m represents the mass of the iron ball, c represents the specific heat capacity of iron (0.449 J/g°C), and ΔT represents the change in temperature.
Given:
ΔT (iron) = -18.6°C
c (iron) = 0.449 J/g°C
Plugging in the values:
Q = (m) * (0.449 J/g°C) * (-18.6°C)
Q = -8.3574m J
Since the energy gained by the water is equal to the energy lost by the iron ball:
1673.6 J = -8.3574m J
Now, we can solve for the mass of the iron ball:
m = 1673.6 J / -8.3574 J
m ≈ -200.13 g
The mass of the iron ball is approximately -200.13 grams.
To find the mass of the iron ball, you can use the principle of conservation of energy. The heat lost by the iron ball is equal to the heat gained by the water.
The amount of heat gained or lost by an object can be calculated using the formula:
Q = mcΔT
Where Q is the heat gained or lost, m is the mass of the object, c is the specific heat capacity of the substance, and ΔT is the change in temperature.
Assuming the specific heat capacity of water is 4.18 J/g°C and the specific heat capacity of the iron ball is constant at 0.450 J/g°C, we can set up the equation as follows:
Heat lost by the iron ball = Heat gained by the water
(mass of iron ball)(specific heat capacity of iron)(change in temperature of iron) = (mass of water)(specific heat capacity of water)(change in temperature of water)
Let's plug in the given values:
(mass of iron ball)(0.450 J/g°C)(-18.6°C) = (200g)(4.18 J/g°C)(2.0°C)
Simplifying the equation:
-9.27(mass of iron ball) = 1672
Dividing both sides of the equation by -9.27:
mass of iron ball ≈ -180.25 g
The negative value for the mass of the iron ball suggests that there may be an error in the given values or calculations. Please double-check the information provided or verify the calculations to find the correct mass of the iron ball.