Calculate amount of energy needed to completely vaporize a 50g piece of 20 degree C silver
melting point 1064 C
L(f) = 64KJ/Kg
Boiling point 2856C
L(v) = 1645 KJ/Kg
c= 0.13KJ/Kg degrees C
I'm thinking I balance each side to equal each other but I'm not dure-I've done specific heat calcs with water-Could you please just tell me how to set it up
Thank you
To calculate the amount of energy needed to completely vaporize a 50g piece of silver, we need to consider the different phases of the substance and the energy required for each phase change.
1. Firstly, we need to calculate the energy required to heat the silver from its initial temperature of 20 degrees Celsius to its melting point of 1064 degrees Celsius. To do this, we can use the formula:
Q = mcΔT
Where:
Q is the heat energy (in joules),
m is the mass of the substance (in kilograms),
c is the specific heat capacity of the substance (in joules per kilogram per degrees Celsius),
ΔT is the change in temperature (in degrees Celsius).
In this case, the mass of silver is 50g, so we need to convert it to kilograms (divide by 1000). The specific heat capacity of silver is given as 0.13 KJ/Kg degrees Celsius. The change in temperature is (1064 - 20) degrees Celsius.
Calculating Q:
m = 50g ÷ 1000 = 0.05kg
ΔT = 1064°C - 20°C = 1044°C
Q = (0.05kg) x (0.13 KJ/Kg degrees Celsius) x (1044°C)
= 67.56 KJ
Therefore, it requires 67.56 KJ of energy to heat the silver from 20 degrees Celsius to its melting point.
2. Next, we need to calculate the energy required for the phase change from solid to liquid, which is called the enthalpy of fusion (L(f)). The enthalpy of fusion for silver is given as 64KJ/Kg.
The total energy required for this phase change can be calculated as:
Q = mL(f)
Where:
m is the mass of the substance (in kilograms),
L(f) is the enthalpy of fusion (in joules per kilogram).
Calculating Q:
m = 0.05kg (since we are still considering the same mass as before)
Q = (0.05kg) x (64KJ/Kg)
= 3.2 KJ
Therefore, it requires an additional 3.2 KJ of energy to completely melt the silver.
3. Finally, we need to calculate the energy required to vaporize the liquid silver. This is called the enthalpy of vaporization (L(v)). The enthalpy of vaporization for silver is given as 1645KJ/Kg.
The total energy required for this phase change can be calculated as:
Q = mL(v)
Using the same mass as before (0.05kg), we can calculate Q:
Q = (0.05kg) x (1645KJ/Kg)
= 82.25 KJ
Therefore, it requires an additional 82.25 KJ of energy to completely vaporize the liquid silver.
To determine the total energy required to completely vaporize the 50g piece of silver, we sum up the energy needed for each step:
Total energy = Energy to heat + Energy for fusion + Energy for vaporization
= 67.56 KJ + 3.2 KJ + 82.25 KJ
= 152.01 KJ
So, it requires a total of 152.01 KJ of energy to completely vaporize a 50g piece of silver starting from 20 degrees Celsius.