a 100 g iron bar at 100 C is placed in 200 g of water at 20 C. If specific heat of iron is 0.11 cal/G*c to what final temperature will the iron bar cool?
To determine the final temperature to which the iron bar will cool, we need to use the concept of heat transfer and the specific heat capacities of iron and water.
Here's how you can calculate it step by step:
1. Calculate the heat absorbed by the water:
The specific heat capacity of water is 1 cal/g°C.
The initial temperature of the water, Twi = 20°C.
The final temperature of the water and the iron bar, Tfin = ?
The mass of the water, mw = 200 g.
The heat absorbed by the water, Qw = mw * 1 cal/g°C * (Tfin - Twi)
2. Calculate the heat released by the iron bar:
The specific heat capacity of iron is 0.11 cal/g°C.
The initial temperature of the iron bar, Ti = 100°C.
The mass of the iron bar, mi = 100 g.
The heat released by the iron bar, Qi = mi * 0.11 cal/g°C * (Ti - Tfin)
3. Since energy is conserved, the heat absorbed by the water is equal to the heat released by the iron bar:
Qw = Qi
mw * 1 cal/g°C * (Tfin - Twi) = mi * 0.11 cal/g°C * (Ti - Tfin)
4. Rearrange the equation to solve for Tfin:
(mw * 1 cal/g°C * Tfin) + (mi * 0.11 cal/g°C * Tfin) = (mi * 0.11 cal/g°C * Ti) + (mw * 1 cal/g°C * Twi)
Factor out Tfin:
Tfin (mw * 1 cal/g°C + mi * 0.11 cal/g°C) = (mi * 0.11 cal/g°C * Ti) + (mw * 1 cal/g°C * Twi)
Solve for Tfin:
Tfin = [(mi * 0.11 cal/g°C * Ti) + (mw * 1 cal/g°C * Twi)] / (mw * 1 cal/g°C + mi * 0.11 cal/g°C)
5. Plug in the given values and calculate:
Tfin = [(100 g * 0.11 cal/g°C * 100°C) + (200 g * 1 cal/g°C * 20°C)] / (200 g * 1 cal/g°C + 100 g * 0.11 cal/g°C)
Tfin = (11,000 cal + 4,000 cal) / (200 cal + 11 cal)
Tfin = 15,000 cal / 211 cal
6. Convert from calories to degrees Celsius:
Tfin ≈ 71.09°C
Therefore, the iron bar will cool to approximately 71.09°C.