In order to raise the temperature of 5.0 Kg of water from 20 degrees C to 30 degrees C,m a 2.0 Kg iron bar is heated and then dropped into the water. what should the starting temperature of the bar be? (specific heat of Fe = 0.11 cal/g-deg.)
heat lost by bar + heat gained by water = 0
[mass Fe x specific heat Fe x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinitial)] = 0
Solve for Tinitial.
Mol
To solve this problem, we can use the concept of heat transfer. The heat gained by the water will be equal to the heat lost by the iron bar.
First, let's calculate the heat gained by the water. We can use the formula:
Q = m * c * ΔT
Where:
Q is the heat gained or lost by the substance (water in this case)
m is the mass of the substance (water in this case)
c is the specific heat capacity of the substance (water in this case)
ΔT is the change in temperature
Given:
m = 5.0 kg (mass of water)
c = 1 cal/g°C (specific heat capacity of water)
ΔT = (30 - 20) °C = 10 °C (change in water temperature)
Now, let's calculate the heat lost by the iron bar. We can use the same formula:
Q = m * c * ΔT
Where:
Q is the heat gained or lost by the substance (iron bar in this case)
m is the mass of the substance (iron bar in this case)
c is the specific heat capacity of the substance (iron in this case)
ΔT is the change in temperature
Given:
m = 2.0 kg (mass of iron bar)
c = 0.11 cal/g°C (specific heat capacity of iron)
ΔT = (final temperature of the water - starting temperature of the bar) °C
Since the heat lost by the iron bar is equal to the heat gained by the water (assuming no heat is lost to the surroundings):
Q_water = Q_iron
By substituting the values we have, we get:
m_water * c_water * ΔT_water = m_iron * c_iron * ΔT_iron
(5.0 kg) * (1 cal/g°C) * (10 °C) = (2.0 kg) * (0.11 cal/g°C) * (ΔT_iron)
Simplifying this equation:
(50 cal/°C) = (0.22 cal/°C) * (ΔT_iron)
Dividing both sides of the equation by (0.22 cal/°C), we get:
ΔT_iron = (50 cal/°C) / (0.22 cal/°C)
ΔT_iron ≈ 227.27 °C
To find the starting temperature of the iron bar, we need to subtract this value from the final temperature of the water:
Starting temperature of the bar = final temperature of the water - ΔT_iron
Starting temperature of the bar = 30 °C - 227.27 °C
Starting temperature of the bar ≈ -197.27 °C
So, the starting temperature of the iron bar should be approximately -197.27 °C.