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

Answer:

A) 1384.6 J/g

b)110.768 MJ

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

$E = (80\times 1000) 1384.6$

   = 110768000 J

   $= 110.768 \times 10^6 J$