Question

Liquid sodium is being considered as an engine coolant. How many grams of liquid sodium (minimum) are needed to absorb 1.00 MJ of energy (in the form of heat) if the temperature of the sodium is not to increase by more than 10.0 °C? Use CP = 30.8 J/(K·mol) for Na(l) at 500 K.

Answer 1

2,637.30 grams of liquid sodium are needed to absorb 1.00 MJ of energy.

Step-by-step explanation:

Molar heat capacity of sodium metal =
`C_p=30.8 J/(K mol)`

Heat required to be absorbed by sodium = Q = 1.00 MJ= 1,000,000 J

Change in temperature required = ΔT =10.0°C = 283.15 K

Moles of sodium required = n

`Q=n* C_p* \Delta T`

`1,000,000 J=n* 30.8 J/(K mol)* 283.15 K`

n = 114.66 moles

Mass of 114.66 moles of sodium:

`114.66 mol* 23 g/mol=2,637.30 g`

2,637.30 grams of liquid sodium are needed to absorb 1.00 MJ of energy.

Answer 2

Energy absorb is calculated as the product of mass, specific capacity and the change in temperature. It is expressed as:

H = nCpΔT

where n is the moles of substance, Cp is the specific heat capacity and ΔT is the change in temperature.

1 x 10^6 J = n ( 30.8 J/k mol )(10 K)
n = 3246.75 mol
mass = 74642.86 g liquid sodium