Thermodynamics - ice->water->steam

[portofino]

Homework Statement

A 8.0 g ice cube at -30 C is in a rigid, sealed container from which all the air has been evacuated.

How much heat is required to change this ice cube into steam at 240 C?

Homework Equations

Q_net = 0 where Q is heat

C1 = Specific heat capacity, ice: 2.050 kJ/kg-K = 2050 J
C2 = Specific heat capacity, water: 4.184 kJ/kg-K = 4184 J
C3 = Specific heat capacity, water vapor: 1.996 kJ/-kgK = 1996 J

L_f = Latent heat fusion, water 334*10^3 J/kg
L_v = Latent heat vaporization, water 2257*10^3 J/kg

Q_net = Q1 + Q2 + Q3 = 0
Q1 = -30deg C ice --> 0deg C ice, Q2 = 0deg C water --> 100deg C water, Q3 = 100deg C vapor --> 240deg C vapor

Q_net = (C1)(M)(T1) + M(L_f) + (C2)(M)(T2) + M(L_v) + (C3)(M)(T3) = 0
M = 6.0 grams = 0.006 kg
T1 = 30 deg
T2 = 100 deg
T3 = 140 deg

The Attempt at a Solution

Q_net = (C1)(M)(T1) + M(L_f) + (C2)(M)(T2) + M(L_v) + (C3)(M)(T3)

= (2050)(0.006)(30) + (0.006)(334*10^3) + (4184)(0.006)(100) + (0.006)(2257*10^3) + (1996)(0.006)(140)

= 369 + 2004 + 2510.4 + 13542 + 1995.16

= 20420.56 Joules

did i account correctly for all the phase changes etc? is my final answer correct? any help appreciated.

thanks

 

[Ygggdrasil]

It looks correct except m = 0.008kg, not 0.006kg.

 

[baba89]

Yes, your approach and calculations are correct. You have accounted for all the phase changes and your final answer of 20420.56 Joules is correct. It is important to consider the specific heat capacities and latent heats for each phase change in order to accurately calculate the amount of heat required for the entire process. Great job!