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 ball
mass ball x specific heat Fe x (Tfinal - Tinitial) + mass H2O x specific heat H2O x (Tfinal - Tinitial) = 0
mass ball x specific heat ball x (-18.6) + 200 x specific heat H2O x (2)
Look up specific heat Fe and specific heat H2O, substitute those numbers and solve for mass Fe ball.
Post your work if you get stuck.
To determine the mass of the iron ball, we can use the principle of energy conservation. The heat lost by the iron ball is equal to the heat gained by the water. We can use the following formula to calculate the heat exchange:
Q = m1 * c1 * ΔT1 = m2 * c2 * ΔT2
where:
Q is the heat transferred (in joules),
m1 is the mass of the iron ball (in grams),
c1 is the specific heat capacity of iron (in J/g·°C),
ΔT1 is the change in temperature of the iron ball (in °C),
m2 is the mass of the water (in grams),
c2 is the specific heat capacity of water (in J/g·°C),
ΔT2 is the change in temperature of the water (in °C).
Given values:
ΔT1 (change in temperature of the iron ball) = -18.6 °C
ΔT2 (change in temperature of the water) = 2.0 °C
m2 (mass of water) = 200 g
c2 (specific heat capacity of water) = 4.184 J/g·°C (approximately)
Using this formula, we can rearrange it to solve for m1 (mass of the iron ball):
m1 = (m2 * c2 * ΔT2) / (c1 * ΔT1)
Now, we can substitute the known values into this formula:
m1 = (200 g * 4.184 J/g·°C * 2.0 °C) / (-18.6 °C)
Simplifying this equation will give us the mass of the iron ball.