A typical heating curve of water is shown below.
There are five separate heats involved in this problem:
- #q_1# = heat required to warm the ice from -15 °C to 0 °C
- #q_2# = heat required to melt the ice to water at 0 °C
- #q_3# = heat required to warm the water from 0 °C to 100 °C
- #q_4# = heat required to boil the water to ice at 1000 °C
- #q_5# = heat required to heat the steam from 100 °C to -105.0 °C
#q = q_1 + q_2 + q_3 +q_4 + q_5#
#= mc_1ΔT_1 + mΔ_text(fus)H + mc_3ΔT_3 + mΔ_text(vap)H + mc_5ΔT_5#
where
#q_1, q_2, q_3, q_4,# and #q_5# are the heats involved in each step
#m# is the mass of the sample
#ΔT = T_"f" -T_"i"#
#c_1color(white)(mm) = "the specific heat capacity of ice" = "0.50 cal·°C"^"-1""g"^"-1"#
#c_3color(white)(mm) = "the specific heat capacity of water" = "1.00 cal·°C"^"-1""g"^"-1"#
#c_5 color(white)(mm)= "the specific heat capacity of steam" = "0.48 cal·°C"^"-1""g"^"-1"#
#Δ_text(fus)H = "the enthalpy of fusion of ice" = "79.5 cal·g"^"-1"#
#Δ_text(vap)H = "the enthalpy of vaporization of water" = "539 cal·g"^"-1"#
#bbq_1#
#ΔT_1 = "0 °C - (-15 °C)" = "15 °C"#
#q_1 = mc_1ΔT_1 = 125.00 color(red)(cancel(color(black)("g"))) × 0.50 color(white)(l)"cal"·color(red)(cancel(color(black)( "°C"^"-1""g"^"-1"))) × 15 color(red)(cancel(color(black)("°C"))) = "938 cal"#
#bbq_2#
#q_2 = 125.00 color(red)(cancel(color(black)("g"))) × 79.5color(white)(l) "cal"·color(red)(cancel(color(black)("g"^"-1"))) = "9938 cal"#
#bbq_3#
#ΔT = "100 °C - 0 °C" = "100 °C"#
#q_3 = mcΔT = 125.00 color(red)(cancel(color(black)("g"))) × 1.00 color(white)(l)"cal"·color(red)(cancel(color(black)( "°C"^"-1""g"^"-1"))) × 100 color(red)(cancel(color(black)("°C"))) = "12 500 cal"#
#bbq_4#
#q_4 = 125.00 color(red)(cancel(color(black)("g"))) × 539color(white)(l) "cal"·color(red)(cancel(color(black)("g"^"-1"))) = "67 380 cal"#
#bbq_5#
#ΔT_5 = "105.0 °C - 1000 °C" = "5.0 °C"#
#q_5 = mcΔT = 125.00 color(red)(cancel(color(black)("g"))) × 0.48 color(white)(l)"cal"·color(red)(cancel(color(black)( "°C"^"-1""g"^"-1"))) × 5.0 color(red)(cancel(color(black)("°C"))) = "300 cal"#
#q = q_1 + q_2 + q_3 + q_4 + q_5 = "938 cal" + "9938 cal" + "12 500 cal" + "67 380 cal" + "300 cal" = "91 000 cal" = "91.0 kcal"#
The process releases 91.0 kcal of heat.
