How much thermal energy is released when 500g of steam at 100° C condenses into water and cools to 50°C

Question

Givens: m=0.5 kg
t = 50
c = 2.010

Qtotal = Q1 + Q2
Qtotal = QmcΔt + mLv
Qtotal = (0.5kg)(2.010)(50) + (0.5)(2.3*10^6)
Qtotal = 1.15 * 10^6

The book says that the answer is 1.3*10^6?
What did I do wrong here?

Answer 1

Lv=2.256E6 J/kg is one error, not 2.3

Secondly, c=4.17J/g or 4180J/kgC is another.

Qtot=.5*4180*50+.5*2.256E6J/kg
= 1.23E6 J
now if you use the erronous 2.3KJ/kg, it becomes 1.25E6 J
then you get into the "significant digits" discourse, which technically should be one (500g, 100C, 50 g), and that gives even a more lubricious answer. Ignore the answer in the book, it was computed by a poorly paid graduate student, or worse.

Answer 2

why is t is 50 though? Isn't the initial temperature is 100 and t final is 50 and therefore, we need to subtract t2-t1 = -50??

Answer 3

The person above is absolutely right, T is (-50). But since the latent heat is being released that makes that value negative too, so it becomes -1.15E6 . So when you add latent heat + mct, the answer is -1.3E6. Whenever you are solving these types of questions, always remember that you add up the heat being released irregardless of the negative or positive sign associated with it to make the question less confusing.

Answer 4

c = 4180 .... thats whats wrong