how much heat energy is needed to change 100 g of ice at 0 ⁰C to water at 30 ⁰C?.

1 Answer
May 18, 2018

#45958# joules.

Explanation:

We use the specific heat equation, which states that,

#q=mcDeltaT#

where:

  • #q# is the heat energy supplied in joules

  • #m# is the mass of the substance

  • #c# is the specific heat capacity of the substance, which is #(4.186 \ "J")/("g" \ ""^@"C")# for water

  • #DeltaT# is the change in temperature

So, we get:

#q=100color(red)cancelcolor(black)"g"*(4.186 \ "J")/(color(red)cancelcolor(black)"g"color(red)cancelcolor(black)(""^@"C"))*30color(red)cancelcolor(black)(""^@"C")#

#=12558 \ "J"#

But then, we also need to change the ice to water first, and so we can use the latent heat formula, which states that,

#q=mL#

  • L# is the latent heat of fusion, vaporization, etc. of the substance

Here, we try to melt ice, so we use #L_f#. (latent heat of fusion)

#:.q=100color(red)cancelcolor(black)"g"*(334 \ "J")/(color(red)cancelcolor(black)"g")#

#=33400 \ "J"#

So, the total energy required is:

#q_"total"=33400 \ "J"+12558 \ "J"#

#=45958 \ "J"#