a 150g-iron ball at 95 Celsius is dropped into a cavity in a block of ice.the cavity is then found to contain 21 g of water . calculate the heat of fusion of ice.

150 C (95-0) = 21 (heat of fusion of ice)

where C is heat capacity of iron about 0.450 J/ g deg c

so the answer would be 305.36 J/G ? is that right?

To calculate the heat of fusion of ice, we need to use the formula:

Q = m·Hf

Where:
Q is the heat absorbed or released during the phase change (in this case, the melting of the ice)
m is the mass of the substance undergoing the phase change (in this case, the mass of the ice/water)
Hf is the heat of fusion, which is a constant value for a specific substance (in this case, the heat of fusion of ice)

First, let's calculate the amount of heat absorbed by the iron ball:

Q_iron = m_iron · c_iron · ΔT

Where:
m_iron is the mass of the iron ball (150g)
c_iron is the specific heat capacity of iron (0.45 J/g·°C)
ΔT is the change in temperature (final temperature - initial temperature)

ΔT = (final temperature of the iron ball) - (initial temperature of the iron ball)
Since the iron ball is dropped into the ice and eventually reaches the same temperature as the ice, the final temperature will be the freezing point of water, 0°C (since the ice would melt at this temperature).

Now, calculating the change in temperature:

ΔT = 0°C - 95°C
ΔT = -95°C

Next, calculating the heat absorbed by the iron ball:

Q_iron = 150g · 0.45 J/g·°C · (-95°C)

Q_iron = -6412.5 J

The negative sign indicates heat release since the iron ball is cooling down.

Since energy is conserved, the heat released by the iron ball will be absorbed by the ice and the water it melts:

Q_iron = Q_ice + Q_water

Now, we need to calculate the heat used to melt the ice:

Q_ice = m_ice · Hf

We're given that the mass of the water formed is 21g, which means that the remaining mass is the mass of the ice:

m_ice = (total mass of ice and water) - (mass of water formed)
m_ice = (150g + 21g) - 21g
m_ice = 150g

Substituting the values in the equation:

-6412.5 J = 150g · Hf

Now, solving for Hf:

Hf = -6412.5 J / 150g

Hf ≈ -42.75 J/g

The negative sign in the answer simply indicates the direction of heat flow. In this case, it implies that the heat is released during the phase change from ice to water. Therefore, the absolute value of heat of fusion is 42.75 J/g.