Question

A gram of water(volume of 1.00cm cubed) at 100 degrees is converted to 1670 centimeters cubed of steam at atmospheric pressure. What is hte change in the internal energy of the water (steam)?

Answer 1

...The internal energy is the sum of all forms of energy.. (says wiki)
So bassically the internal energy is increased because of heat that makes water expand. Although you should wait for someone smarter to answer.

Answer 2

U - internal energy
Delta U - cange of internal energy
m - mass
t1 - starting temperature
t2 - temperature at given momment
c -"specific heat-realted constant for given material" (don't know how to translate) for water it is 4.2 kJ/(kg / Celcius)
Q -"Heat amount"

Delta U = - Q (if Heat is radiated, in your case it is gained so it will be + Q )
Q=c*m*(t2-t1)
So ..
Delta U = c*m*(t2-t1))

Answer 3

How does the latent heat of vaporization's heat release fit into this calculation?

Answer 4

Yeah you are right, it's far from what you actually need and yes, it doesn't fit. You can actually ignore what I have sayed before.

The idea is that convertion from water into steam consume energy. Energy consumed can be calcuted like this

Q = Lm

L -latent heat of vaporization.

But then I'm not sure why are you given the cubed centimeters (from my experience if you are given numbers then you have to use it).

Answer 5

The steam was given in cubed centimeters instead of mass, so you have to calculate the mass of the steam from what is given.

Answer 6

Last resort - Ideal gas law .

PV = n*R*T

P - Pressure
V- Volume
n- amount of substance
R- ideal gas constant (8.3144621(75) J/ mol K)
T - absolute temperature
M - molar mass (i guess it's 18 g/mol for water)
And you get
n = (R*T) / (P*V)
while
n= m/M
and
m= Mn =(M*R*T)/(P*V)
so
Q = 9L*M*R*T) / (P*V)

Answer 7

* last line Q = (L*M*R*T) / (P*V)

Answer 8

Thanks. I will plug in the numbers and work out the solution.