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 heat required to melt 50 g of mercury at -45 degrees Celsius to 425 degrees Celsius, we need to consider the different phases and temperatures involved.
1. Heat required to raise the temperature of solid mercury from -45 degrees Celsius to its melting point:
First, we need to calculate the heat required to raise the temperature from -45 degrees Celsius to the melting point of -38 degrees Celsius. We can use the specific heat capacity of solid mercury, which is given as 0.03325 cal/g-degree Celsius.
Heat required = mass * specific heat * temperature change
Heat required = 50 g * 0.03325 cal/g-degree C * (melting point - initial temperature)
Heat required = 50 g * 0.03325 cal/g-degree C * (-38 C - (-45 C))
Heat required = 50 g * 0.03325 cal/g-degree C * 7 C
Heat required = 11.5875 cal
2. Heat required to melt solid mercury:
To convert solid mercury to liquid mercury at its melting point, we need to consider the heat of fusion, which is given as 2.7 cal/g.
Heat required = mass * heat of fusion
Heat required = 50 g * 2.7 cal/g
Heat required = 135 cal
3. Heat required to raise the temperature of liquid mercury from its melting point to 425 degrees Celsius:
Next, we need to calculate the heat required to raise the temperature of liquid mercury from the melting point (-38 degrees Celsius) to 425 degrees Celsius. We can use the specific heat capacity of liquid mercury, which is given as 0.2988 cal/g-degree Celsius.
Heat required = mass * specific heat * temperature change
Heat required = 50 g * 0.2988 cal/g-degree C * (425 C - melting point)
Heat required = 50 g * 0.2988 cal/g-degree C * (425 C - (-38 C))
Heat required = 50 g * 0.2988 cal/g-degree C * 463 C
Heat required = 6859.4 cal
4. Heat required for vaporization of liquid mercury at 425 degrees Celsius:
To convert liquid mercury to gaseous mercury at 425 degrees Celsius, we need to consider the heat of vaporization, which is given as 65 cal/g.
Heat required = mass * heat of vaporization
Heat required = 50 g * 65 cal/g
Heat required = 3250 cal
Total heat required:
Total heat required = Heat required for temperature change + Heat required for fusion + Heat required for vaporization
Total heat required = 11.5875 cal + 135 cal + 6859.4 cal + 3250 cal
Total heat required = 10255.9875 cal
Therefore, the total heat required to melt 50 g of mercury from -45 degrees Celsius to 425 degrees Celsius is approximately 10255.99 calories.