Question #23a55

1 Answer
Sep 22, 2015

Answer:

#q = -2.52 * 10^3"kcal"#

Explanation:

The idea here is that you need to take into account the heat given off when that much water goes from steam at #100^@"C"# to liquid at #100^@"C"#, and the heat given off when the liquid water is cooled from #100^@"C"# to #10^@"C"#.

You need to know the enthalpy of condensation of water, which tells you how much heat is given off when #"1 g"# of liquid water #100""^@"C"# is converted to steam at #100""^@"C"#

#DeltaH_"con" = -"2260 J/g"#

Like wise, you need to know the specific heat of liquid water, which will tell you how much heat is needed to increase the temperature of #"1 g"# of water by #1""^@"C"#

#c_"water" = 4.184"J"/("g" ^@"C") = 1"cal"/("g"^@"C")#

So, start by calculating how much heat is given off when you turn that much water from steam at #100""^@"C"# to liquid at #100""^@"C"#.

#q_1 = m * DeltaH_"con"#

#q_1 = 4.00color(red)(cancel(color(black)("kg"))) * (1000color(red)(cancel(color(black)("g"))))/(1color(red)(cancel(color(black)("kg")))) * (-2260"J"/color(red)(cancel(color(black)("g")))) = -9.04 * 10^6"J"#

Now calculate how much heat is given off when the water cools

#q_2 = m * c_"water" * DeltaT#

#q_2 = 4.00 * 10^3color(red)(cancel(color(black)("g"))) * 1"cal"/(color(red)(cancel(color(black)("g"))) color(red)(cancel(color(black)(""^@"C")))) * (10 - 100)color(red)(cancel(color(black)(""^@"C"))) = -3.6 * 10^5"cal"#

Convert the first heat from Joules to calories

#-9.04 * 10^6color(red)(cancel(color(black)("J"))) * "1 cal"/(4.184color(red)(cancel(color(black)("J")))) = -2.16 * 10^6"cal"#

The total amount of heat given off will be

#q_"total" = q_1 + q_2#

#q_"total" = -2.16 * 10""^6"cal" - 3.6 * 10""^5"cal" = -2.52 * 10""^6"cal"#

Finally, convert the result from calories to kilocalories

#-2.52 * 10^6color(red)(cancel(color(black)("cal"))) * "1 kcal"/(10^3color(red)(cancel(color(black)("cal")))) = color(green)(-2.52 * 10""^3"kcal")#