How much heat is required to heat 28 g of
solid silver from 130
◦
C to liquid silver at
961
◦
C? The specific heat of solid silver is
0.235 J/g ·
◦
C, and the heat of fusion of silver at its melting point of 961
◦
C is 11.3 kJ/g.
Answer in units of kJ
q1 = heat to raise T from 130 to 961.
q1 = mass Ag x specific heat solid Ag x (Tfinal-Tinitial) [Note: Tfinal is 961).
q2 = heat to melt Ag at 961C.
q2 = mass Ag x heat fusion.
Total q = q1 + q2
14820
5850.18
To determine the amount of heat required to heat solid silver from 130°C to liquid silver at 961°C, we need to consider two steps: heating the solid silver and then melting it.
Step 1: Heating the solid silver:
The specific heat capacity (C) of solid silver is given as 0.235 J/g·°C. To calculate the heat energy (Q) required to raise the temperature of the silver from 130°C to its melting point, we can use the formula:
Q = m * C * ΔT
Where:
Q is the heat energy (in Joules),
m is the mass of the silver (28 g),
C is the specific heat capacity of silver (0.235 J/g·°C),
ΔT is the change in temperature (961°C - 130°C).
Q = 28 g * 0.235 J/g·°C * (961°C - 130°C)
Step 2: Melting the silver:
The heat of fusion of silver is given as 11.3 kJ/g. Since the mass of the silver remains the same during this phase change, we can calculate the heat energy using the formula:
Q = m * ΔH
Where:
Q is the heat energy (in Joules),
m is the mass of the silver (28 g),
ΔH is the heat of fusion of silver (11.3 kJ/g).
Q = 28 g * 11.3 kJ/g
Now, we can calculate the total heat energy required by adding the heat energy from the two steps:
Total Q = Q1 + Q2
Total Q = Q(heating) + Q(melting)
To convert the units from Joules to kilojoules:
1 kJ = 1000 J
So, to get the answer in kJ, you can divide the total heat energy (in Joules) by 1000.
Finally, we can calculate the answer by substituting the values:
Total Q = [(28 g * 0.235 J/g·°C * (961°C - 130°C)) + (28 g * 11.3 kJ/g)] / 1000
After performing the calculations, the answer will be in units of kilojoules (kJ).