Since your question lacks the starting temperature of the ice, I'll pick one myself. So, I assumed that the initial temperature of the ice is #-20^@"C"#.
You have to calculate the energy needed to go from ice at #-20^@"C"# to ice at #0^@"C"#, then to go from ice at #0^@"C"# to water at #0^@"C"#, then finally from water at #0^@"C"# to water at #10^@"C"#.
There are a couple of constants you must use in order to be able to solve this problem
Heat of fusion of water: #DeltaH_f# = #334# #"J/g"#
Specific heat of ice: #c# = #2.09# #"J"#/#"g"^@"C"#;
Specific heat of water: #c# = #4.18# #"J"#/#"g"^@"C"#;
So, in order, the steps you're going to go through are
- Calculate the heat required to go from ice at #-20^@"C"# to ice at #0^@"C"#
#q_1 = m * c_"ice" * DeltaT_1#, where
#m# - the mass of the ice;
#DeltaT_1# - the change in temperature, defined as #T_"final"# minus #T_"initial"#;
#c_"ice"# - the specific heat of ice;
#q_1 = 20cancel("g") * 2.09"J"/(cancel("g") * ^@cancel("C")) * (0 - (-20))^@cancel("C")#
#q_1 = "836 J"#
- Calculate the heat required to go from ice at #0^@"C"# to water at #0^@"C"#
#q_2 = m * DeltaH_f#, where
#DeltaH_f# - the heat of fusion of water;
#q_2 = 20cancel("g") * 334"J"/cancel("g") = "6680 J"#
- Calculate the heat required to go from water at #0^@"C"# to water at #10^@"C"#
#q_3 = m * c_"water" * DeltaT_3#
#q_3 = 20cancel("g") * 4.18"J"/(cancel("g") * ^@cancel("C")) * (10 - 0)^@cancel("C")#
#q_3 = "836 J"#
The total heat required will be
#q_"total" = q_1 + q_2 + q_3#
#q_"total" = "836 J" + "6680 J" + "836 J" = "+8352 J"#
Expressed in kJ and rounded to one sig fig, the answer will be
#q_"total" = color(green)("+8 kJ")#
