Physics: Calorimetry

Question

Calorimetry

a. How much heat needs to be taken from 0.5 kg of ethyl alcohol as a gas at its boiling point of 78.0 C to a solid at its freezing point -114 C if the latent heat of vaporization is 850,000 J/kg and its latent heat of fusion is 104,000 J/kg, and the specific heat is 2400 J/(kg C).

b. If an piece of Iron (c = 450 J/kg C) at 65.0 C is dropped into .250 kg of ethyl alcohol at 25.0 C and the final temperature of the two comes to 35.0 C what was the mass of the piece of iron?

c. If .35 kg of solid ethyl alcohol at -114.0 C is put in a large well insulated jug holding 2.5 kg of liquid ethyl alcohol initially at 35.0 C what will the final temperature be after all the solid form has melted and come to equilibrium?

Answer 1

a)  heat = (m)ΔH_fusion + (m)(c_p)(ΔT) + (m)ΔH_vap = (0.5)(104,000) + (.5)(2400)(78.0 - (-114)) + (0.5)(850,000)

= 52,000 + 230,400 + 425,000 = 707,400 J

 

b)  heat lost = heat gained  -->  m₁c_p1(T₁ - T_F) = m₂c_p2(T_F - T₂)  -->  m₁ = (m₂c_p2(T_F - T₂)) / (c_p1(T₁ - T_F))

-->  m₁ = ((0.250)(2400)(35.0 - 25.0)) / ((450)(65.0 - 35.0)) = 0.444 kg

 

c)  heat gained = heat lost  -->  m₁ΔH_fusion + m₁c_p(T_F - T₁) = m₂c_p(T₂ - T_F)  -->  m₁c_pT_F + m₂c_pT_F = -m₁ΔH_fusion + m₂c_pT₂ + m₁c_pT₁  -->  T_F = (-m₁ΔH_fusion + m₂c_pT₂ + m₁c_pT₁) / (m₁c_p + m₂c_p)  -->

T_F = ((-0.35)(104,000) + (2.5)(2400)(35.0) + (.35)(2400)(-114)) / ((.35)(2400) + (2.5)(2400)) = 11.4 C