What is the mass of a sample of water that takes 2000 kJ of energy to boil into steam at 373 K? The latent heat of vaporization of water is [tex]$225 \times 10^3 kg^{-1}$[/tex].
A. 0.0088 kg
B. 0.24 kg
C. 0.88 kg
D. 1.13 kg
Answer (1)
Use the formula for latent heat: Q = m L .
Rearrange the formula to solve for mass: $m =
rac{Q}{L}$.
Substitute the given values: $m =
rac{2000
imes 10^3}{2.25
imes 10^6}$.
Calculate the mass: $m
approx 0.88 kg$.
Explanation
Understanding the Problem We are given the energy required to boil a sample of water into steam and the latent heat of vaporization of water. We need to find the mass of the water sample.
Stating the Formula The energy required to change the phase of a substance is given by the formula: Q = m L where:
Q is the energy required (in Joules),
m is the mass of the substance (in kg),
L is the latent heat of vaporization (in J/kg).
Identifying Given Values We are given:
$Q = 2000 kJ = 2000
imes 10^3 J = 2,000,000 J$
$L = 2.25
imes 10^6 J/kg W e n ee d t o f in d m$.
Calculating the Mass Rearrange the formula to solve for m :
m = r a c Q L Substitute the given values: m = r a c 2 , 000 , 000 J 2.25 im es 1 0 6 J / k g m = r a c 2 , 000 , 000 2 , 250 , 000 k g m = r a c 2000 2250 k g m = r a c 200 225 k g m = r a c 40 45 k g m = r a c 8 9 k g ma pp ro x 0.8889 k g
Final Answer The mass of the water sample is approximately 0.8889 kg. Looking at the multiple-choice options, the closest value is 0.88 kg.
Examples
Latent heat and phase change calculations are crucial in many real-world applications. For example, understanding the energy required to vaporize water is essential in designing efficient cooling systems for power plants. Similarly, knowing the heat of fusion helps in designing effective thermal storage systems that utilize phase change materials to store and release energy. These principles are also applied in meteorology to understand cloud formation and precipitation processes, as well as in cooking to understand how different foods cook at different temperatures.
