How much water at 20 degrees C is needed to melt 1 kg of solid mercury at its melting point which is -39 degrees C? (The heat of fusion of mercury is 2.8 cal/gram).
To calculate the amount of water needed to melt 1 kg of solid mercury, we need to consider the heat transfer between the water and the solid mercury during the melting process.
First, we need to determine the amount of heat required to melt 1 kg of solid mercury. The heat of fusion, given as 2.8 cal/gram, represents the amount of heat required to convert one gram of solid mercury into liquid mercury at its melting point.
Since we have 1 kg (1000 grams) of solid mercury, we can calculate the total heat required for melting as follows:
Heat required = (heat of fusion) x (mass of solid mercury)
= 2.8 cal/gram x 1000 grams
= 2800 cal
Next, we need to consider the heat transfer from the water to the solid mercury. Since the solid mercury is at -39 degrees C and we want it to reach 20 degrees C, we need to calculate the amount of heat transferred to raise the temperature from -39 degrees C to 0 degrees C, considering the specific heat capacity of mercury.
The specific heat capacity of mercury is approximately 0.0336 cal/gram °C.
Heat transfer required = (specific heat capacity) x (mass of solid mercury) x (change in temperature)
= 0.0336 cal/gram °C x 1000 grams x 39 °C
= 1310.4 cal
Now, we can calculate the total heat required to melt 1 kg of solid mercury and raise its temperature to 0 degrees C:
Total heat required = Heat required for melting + Heat transfer required
= 2800 cal + 1310.4 cal
= 4110.4 cal
Assuming no heat losses to the surroundings, we need to supply 4110.4 calories of heat to the solid mercury to melt it completely.
Now, we can determine the amount of water required to provide this heat. The heat absorbed or released by water can be calculated using the specific heat capacity of water, which is approximately 1 cal/gram °C.
We will assume the initial temperature of water is the same as the melting point of solid mercury (-39 degrees C).
Heat absorbed by water = (specific heat capacity of water) x (mass of water) x (change in temperature)
We need to convert the heat required into calories by dividing by 1000.
Since we know the heat required and the initial and final temperatures of the water, we can rearrange the equation to solve for the mass of water:
Mass of water = (Heat absorbed by water) / [(specific heat capacity of water) x (change in temperature)]
Mass of water = (4110.4 cal) / [(1 cal/gram °C) x (20 °C - (-39) °C)]
= 4110.4 / (1 x 59)
≈ 69.7 grams
Therefore, approximately 69.7 grams of water at 20 degrees C are needed to melt 1 kg of solid mercury at its melting point.