Answer:
The temperature of the final equilibrium temperature of the system is 19.7⁰C
Explanation:
Given;
mass of the ice, m₁ = 25 kg
temperature of the ice = 0°C
mass of the steam, m₂ = 4 kg
temperature of the steam, = 100 ⁰C
Let the temperature of the resulting mixture = t
Apply the principle of conservation of energy.
Heat required to melt the ice + Heat gained by the mixture = Heat required to convert the water to steam + Heat lost by the mixture
[tex]m_1L_f + m_1c (t - 0) = m_2L_v + m_2c(100 - t)[/tex]
where;
Lf is the latent heat of fusion of ice = 3.33 x 10⁵ J/kg.
Lv is the latent heat of vaporization of water, = 2.260 x 10⁶ J/kg
c is the specific heat capacity of water = 4,200 J/kg
[tex]m_1L_f + m_1c (t - 0) = m_2L_v + m_2c(100 - t)\\\\25 \times 3.33\times 10^5 + 25\times 4,200 (t ) = 4\times 2.26\times 10^6 + 4\times 4,200(100 - t)\\\\8,325,000 + 105,000t = 9,040,000 + 1,680,000 - 16,800t\\\\105,000t + 16,800t = 10,720,000 - 8,325,000\\\\121,800t = 2,395,000\\\\t = \frac{2,395,000}{121,800} \\\\t = 19.7 \ ^0 C[/tex]
The temperature of the final equilibrium temperature of the system is 19.7⁰C
