To determine the minimum amount of liquid sodium required to absorb 900 MJ of energy, we first need to know the specific heat capacity of liquid sodium. The specific heat capacity of sodium is approximately 1.23 J/g·K.
Next, we can use the formula:
Q = mcΔT
Where:
- Q is the heat energy (in joules),
- m is the mass in grams,
- c is the specific heat capacity (in J/g·K),
- ΔT is the change in temperature (in K).
Rearranging the formula to solve for mass, we have:
m = Q / (cΔT)
Assuming we want to find the minimum mass of sodium to absorb 900 MJ (which is 900,000,000 J) with a certain change in temperature ΔT, we can express the mass in relation to temperature change as:
m = 900,000,000 J / (1.23 J/g·K * ΔT)
From this formula, we can observe that:
– If we choose a specific ΔT, we can calculate the required mass.
For example, if we take a moderate temperature change of 100 K:
m = 900,000,000 J / (1.23 J/g·K * 100 K) = 731,707.32 g
Thus, a minimum of approximately 731,707.32 grams of liquid sodium would be required to absorb 900 MJ of heat energy with a 100 K change in temperature.
In summary, the amount of liquid sodium needed will vary depending on the desired temperature change; hence, you can adjust the ΔT in the equation to find different mass values as required.