Liquid sodium is being considered as an engine coolant. how many grams of liquid sodium (minimum)are needed to absorb 3.60 MJ of energy(in the form of heat) if the temperature of the sodium is not to increase by more than 10.0 degree celcius? use Cp=30.8 J/(K.mol) for Na(l) at 500 k.
heat=moles*Cp*deltatemp
heat*atomicmass=mass*Cp*deltaTEmp
mass=3.6e6*23/(30.8*10) grams
To calculate the minimum amount of liquid sodium required to absorb 3.60 MJ of energy, we need to use the equation:
Q = mcΔT
Where:
Q = amount of energy absorbed (in Joules)
m = mass of sodium (in grams)
c = specific heat capacity of sodium (in J/(g·°C))
ΔT = change in temperature (in °C)
First, we need to convert 3.60 MJ to Joules:
3.60 MJ = 3.60 × 10^6 J
Next, we rearrange the equation to solve for the mass of sodium (m):
m = Q / (cΔT)
Now, let's substitute the given values into the equation:
m = (3.60 × 10^6 J) / (30.8 J/(g·°C) × 10.0 °C)
Simplifying the equation:
m = (3.60 × 10^6 J) / (308 J/g)
m = 11,688 g
Therefore, a minimum of 11,688 grams of liquid sodium is needed to absorb 3.60 MJ of energy without increasing its temperature by more than 10.0 degrees Celsius.