What mass of carbon can 3000 J of energy raise from 12°C to 40°C?

The answer to your question is mass = 0.824 kg or mass = 82.4 g

Explanation:

Data

Mass = m

Energy = E = 3000 J

Temperature 1 = T1 = 12°C

Temperature 2 = T2 = 40°C

Specific heat of C = 1300 kJ/kg°K

Process

1.- Convert temperature to Kelvin

T1 = 273 + 12 = 285°K

T2 = 273 + 40 = 313°K

2.- Substitution

       Energy = m C (T2 - T1)

- Solve for m

       mass = Energy / C(T2 - T1)

       mass = 3000 / 1300 (313 - 285)

       mass = 3000 / 1300(28)

       mass = 3000 / 36400

      mass = 0.082 kg

or    mass = 82.4 g

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3