Question

The melting temperature of pure titanium = 1668°C, its density = 4.5 g/cm^3, specific heat = 0.544 J/gºC, and heat of fusion = 419 J/g. Assume specific heat has the same value for solid and molten metal. The pouring temperature for titanium is 1800°C, and the starting temperature = 25°C. Estimate the (a) energy for heating unit mass (1 g pure titanium) to pouring temperature and (b) total energy to heat 80 kg of the metal.

Answer 1

A) 1384.6 J/g

b)110.768 MJ

Step-by-step explanation:

Given data:

`T_(melting) = 1668 degree C`

density of titanium = 4.5 g/cm^3

specific heat = 0.544 J/g degree C

heat of fusion = 419 J/g

Pouring temperature for titanium = 1800 degree C

Initial temperature = 25 degree C

a) eneegy for heating unit mass is given as

`E = C(T_(melting) - T_(initial)) + L + C(T_(pouring) - T_(melting))`

`= 0.544(1668-25) + 419 + 0.544(1800-1668)`

= 1384.6 J/g

b) Total energy to heat 80 kg metal

we know for one unit 1384.6 J/g energy is required

therefore for 80 kg , energy required is

`E = (80* 1000) 1384.6`

= 110768000 J

`= 110.768 * 10^6 J`