Question #f9d73

1 Answer
Jun 1, 2015

You'd need 4.7 kJ of heat to convert that much solid aluminium to fully molten at its melting point.

You start with a sample of solid aluminium at #580.0^@"C"#. In order to get the aluminium from solid to molten, you're going to have to supply enough heat to get it

  • Go from solid at #580.0^@"C"# to solid at #660.4^@"C"#;

You know that

#q_1 = m * c * DeltaT#, where

#q_1# - the heat supplied to the metal;
#m# - the mass of the metal;
#c# - the specific heat of the metal;
#DeltaT# - the change in temperature, defined as the final temperature minus the initial temperature.

Plug in your values and solve for #q_1#.

#q_1 = 10.0cancel("g") * 0.89"J"/(cancel("g") ^@cancel("C")) * (660.4-580.0)cancel("K")#

#q_1 = "715.7 J"#

  • Go from solid at #660.4^@"C"# to molten at #660.4^@"C"#.

This time, the sample is undergoing a phase change, i.e. it goes from solid to molten. This transition happens at constant temperature, so the equation you're going to use is

#q_2 = m * DeltaH_"fus"#, where

#DeltaH_"fus"# - the enthalpy of fusion;

Once again, plug your values into the equation and solve for #q_2#

#q_2 = 10.0cancel("g") * 398"J"/cancel("g") = "3980 J"#

The total heat required will be equal to

#q_"total" = q_1 + q_2#

#q_"total" = 715.7 + 3980 = "4695.7 J"#

Rounded to two sig figs and expressed in kJ, the answer will be

#q_"total" = color(green)("+4.7 kJ")#

SIDE NOTE The + sign shows that the heat is supplied to the metal.