One of the largest diamonds ever found, weighing 0.621 kg, was discovered in South Africa in 1905. The carbon alloptropes graphite and diamond have densities of 2267 and 3515 kg/m3 respectively. At a temperature of 1700K and a pressure of 12.0 x 109 Pascals graphite becomes diamond. Estimate the amount of work that would be needed to form this large diamond from graphite.
the answer is suppose to be 1.17 x10^3 kj
how do i do this question?
using the mass of the diamond
... find the volume of a graphite sphere and a diamond sphere
the pressure compresses the graphite sphere into the diamond sphere
... by pushing on the surface area, through the difference in the radii
the work is an integral function, but you can do a linear approximation
Would it be as easy (or easier) to convert the densities to volume, then use work = p*dV
To solve this question, you need to calculate the work needed to convert the graphite (starting material) into diamond (final product). In order to do this, you need to consider the change in volume and pressure, as well as the equation for work done under constant pressure.
Here's how you can approach the problem step by step:
1. Determine the change in volume:
The density of graphite is given as 2267 kg/m3, and that of diamond is given as 3515 kg/m3. Since the density is mass/volume, you can calculate the volume of graphite and diamond:
Volume of graphite: V_graphite = m_graphite / ρ_graphite
= 0.621 kg / 2267 kg/m3
Volume of diamond: V_diamond = m_diamond / ρ_diamond
= 0.621 kg / 3515 kg/m3
2. Calculate the change in volume:
The change in volume (ΔV) can be found by subtracting the initial volume (V_graphite) from the final volume (V_diamond):
ΔV = V_diamond - V_graphite
3. Use the ideal gas law to find the number of moles:
Since pressure (P) and temperature (T) are given, we can use the ideal gas law to find the number of moles (n):
PV = nRT
Here, R is the ideal gas constant and its value is 8.314 J/(mol·K). Rearrange the equation to solve for n:
n = PV / RT
4. Calculate the work done:
The work (W) done during this conversion process can be calculated using the equation:
W = -PΔV
Here, -P represents the negative of the pressure, and ΔV is the change in volume we calculated earlier.
5. Convert the work to kilojoules:
The final step is to convert the work from joules to kilojoules by dividing the value by 1000.
By following these steps, you should be able to calculate the work needed to form the diamond from graphite. The answer should be approximately 1.17 x 103 kJ.