Q: Calculate the amount of energy in Joules required to change 10 g of solid mercury at its melting point to mercury vapor at the boiling point. The m_p, b_p, and specific heat of mercury are -39^degree C, 375^degree C, and 0.140 J/g^degree C, respectively. Compare with the amount of heat needed to change 10 g of ice at 0^degree C to steam at 100^degree C.
Answer:
The heat required = 575.4 J
Q₂ > Q₁ (The amount of energy required by the mercury is small than the amount of energy required by the water.)
Explanation:
Q₁ = c₁m₁(T₂-T₁)....................... Equation 1
Where Q₁ = amount of heat or Energy. c₁ = specific heat capacity of mercury, m₁ = mass of mercury, T₂ = Temperature of mercury at boiling point, T₁ = Temperature of mercury at melting point.
Given: m₁ = 10 g , c₁ = 0.14 J/g.°C, T₂ = 372 °C, T₁ = -39 °C
Substituting these values into equation 1
Q₁ = 10×0.14 (372+39)
Q₁ = 1.4(411)
Q₁ = 575.4 J.
Thus the heat required = 575.4 J
Q₂ = c₂m₂(θ₂-θ₁)....................... Equation 2
Where Q₂ = heat required to change the temperature of water from 0 °C to 100 °C, c₂ = specific heat capacity of water, m₂ = mass of water, θ₂ = Final temperature of water, θ₁ = Initial Temperature of water.
Given: m₁ = 10 g, θ₂ = 100 °C, θ₁ = 0 °C
Constant: c₂ = 4.2 J/g.°C
Substituting these values into equation 2
Q₂ = 10(4.2)(100-0)
Q₂ = 4200 J.
Comparing Q₁ and Q₂,
Q₂ > Q₁
Hence the amount of energy required by the mercury is small than the amount of energy required by the water.
