An iron ball weighing 200 gm and specific heat of 0.11 is removed from a furnace and dropped into 550 gm of water at 5 degrees Celsius and the water is heated to 5 degrees Celsius. What must have been the temperature of the furnace?
To determine the temperature of the furnace, we can use the principle of conservation of energy. The heat lost by the iron ball when it cools down will be gained by the water as it heats up.
The formula to calculate the heat exchanged between an object and the surrounding is:
Q = m * c * ΔT
Where:
Q: Heat exchanged
m: Mass of the object
c: Specific heat
ΔT: Change in temperature
The heat lost by the iron ball will be equal to the heat gained by the water, so we can equate the two equations:
Q(iron ball) = Q(water)
m(iron ball) * c(iron ball) * ΔT(iron ball) = m(water) * c(water) * ΔT(water)
Substituting the given values:
200 gm * 0.11 * (Tf - 5°C) = 550 gm * 1 * (100°C - Tf)
Where:
Tf: Temperature of the furnace (unknown)
Now, we can solve this equation to find the value of Tf.
200 * 0.11 * Tf - 200 * 0.11 * 5 = 550 * (100 - Tf)
22Tf - 1100 = 55000 - 550Tf
572Tf = 56100
Tf = 56100 / 572
Tf ≈ 98.08°C
Therefore, the temperature of the furnace must have been approximately 98.08°C.