How much heat is required to melt 50 g of mercury at -45 degrees celsius to 425 degrees celsius. (melting point=-38.degree-c, specific heat=0.03325 cal/g-degree c for solid mercury, .2988 cal/g-c degree c for liquid mercury and .2486 cal/g-c degree for gaseous mercury, heat of fusion =2.7 cal/g, heat of vaporization=65 cal/g)
To calculate the amount of heat required to melt a substance, we need to consider the following steps:
1. Calculate the heat required to warm the solid mercury from -45°C to its melting point of -38°C.
2. Calculate the heat required to melt the solid mercury at its melting point.
3. Calculate the heat required to warm the liquid mercury from its melting point to 425°C.
Step 1: Calculate the heat required to warm the solid mercury from -45°C to -38°C.
The heat required to raise the temperature of a substance can be calculated using the formula:
Q = m * c * ΔT
Where:
Q is the heat required (in calories)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in cal/g-°C)
ΔT is the change in temperature (in °C)
In this case, the mass of mercury is 50 g, the specific heat capacity of solid mercury is 0.03325 cal/g-°C, and the change in temperature is (-38°C - (-45°C)) = 7°C.
So, the heat required to warm the solid mercury from -45°C to -38°C is:
Q1 = 50 g * 0.03325 cal/g-°C * 7°C = 11.6375 cal
Step 2: Calculate the heat required to melt the solid mercury at its melting point.
The heat required to melt a substance can be calculated using the formula:
Q = m * ΔHf
Where:
Q is the heat required (in calories)
m is the mass of the substance (in grams)
ΔHf is the heat of fusion of the substance (in cal/g)
In this case, the mass of mercury is 50 g, and the heat of fusion of mercury is 2.7 cal/g.
So, the heat required to melt the solid mercury at its melting point is:
Q2 = 50 g * 2.7 cal/g = 135 cal
Step 3: Calculate the heat required to warm the liquid mercury from its melting point to 425°C.
The heat required to raise the temperature of a substance can be calculated using the same formula as in Step 1.
In this case, the mass of mercury is 50 g, the specific heat capacity of liquid mercury is 0.2988 cal/g-°C, and the change in temperature is (425°C - the melting point of mercury at 0°C).
So, the heat required to warm the liquid mercury from its melting point to 425°C is:
Q3 = 50 g * 0.2988 cal/g-°C * (425°C - 0°C) = 6342 cal
Finally, to calculate the total heat required, we sum up the heat required for each step:
Total heat required = Q1 + Q2 + Q3 = 11.6375 cal + 135 cal + 6342 cal = 6488.6375 cal
Therefore, approximately 6489 calories of heat are required to melt 50 grams of solid mercury at -45°C to 425°C.