A 63.8 kg block of silver is at initially at 107 C. 1.0 kg of ice at its freezing point is placed onto the block to cool it. As the ice melts, the water is free to flow off (so that the water never increases in temperature). After all the ice melts, what is the final temperature of the silver? Round answers to the nearest whole number, and in degrees Celsius.

water - 4.2*10^3, latent fusion; 3.3*10^2
silver- heat cap. 0.24 J/°C·g

See other post, modify constants to suit given values. Give final answer to 2 significant figures.

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To find the final temperature of the silver block after the ice melts, we need to calculate the amount of heat transferred between the silver and the ice. We can then use this heat transfer to determine the final temperature.

First, let's calculate the heat transferred from the silver block to the ice during the cooling process.

The heat transferred from the silver block is given by the equation:
Q_silver = m_silver * c_silver * ΔT_silver

Where:
m_silver is the mass of the silver block (63.8 kg),
c_silver is the specific heat capacity of silver (0.24 J/°C·g), and
ΔT_silver is the change in temperature of the silver block.

The heat that needs to be transferred from the silver block to the ice is equal to the heat required to melt the ice. This is calculated using the formula:

Q_melting = m_ice * L_fusion

Where:
m_ice is the mass of the ice (1.0 kg), and
L_fusion is the specific latent fusion heat of ice (3.3*10^2 J/g).

Next, we equate the two heat transfers (Q_silver = Q_melting) and solve for ΔT_silver:

m_silver * c_silver * ΔT_silver = m_ice * L_fusion

Now, let's plug in the given values and calculate ΔT_silver:

(63.8 kg) * (0.24 J/°C·g) * ΔT_silver = (1.0 kg) * (3.3*10^2 J/g)

(63.8 kg) * (0.24 J/°C·g) * ΔT_silver = (1.0 kg) * (3.3*10^2 J/g)

ΔT_silver = (1.0 kg) * (3.3*10^2 J/g) / (63.8 kg * 0.24 J/°C·g)

ΔT_silver ≈ 5.235°C

Therefore, the change in temperature of the silver block is approximately 5.235°C.

Finally, to find the final temperature of the silver block, we subtract the change in temperature from the initial temperature:

Final temperature = Initial temperature - ΔT_silver
Final temperature ≈ 107°C - 5.235°C
Final temperature ≈ 101°C

Therefore, the final temperature of the silver block after the ice melts is approximately 101°C.