Question

to answer this question, first click here to view the associated video. does it take more, less, or the same amount of heat to melt 1.0 kg of ice at t = 0°c, or to bring 1.0 kg of liquid water at 0°c to the boiling point? assume that, for water, c = 4186 j/(kg·°c) and l_f = 3.35×10⁵ j/kg. ○ less. ○ the same. ○ more. you drop a large ice cube into a glass of water at 85.0°f. after some stirring, you notice that the ice starts to melt. assuming the water/ice reaches thermal equilibrium, which statement is true regarding the temperature of the water? ○ t = 32°f ○ 0°f < t < 32°f ○ 32°f < t < 85°f ○ t = 0°f

Explanation:

Step1: Calculate heat to melt ice

The heat required to melt ice is given by \(Q_{melt}=mL_F\).
Substituting \(m = 1.0\space kg\) and \(L_F=3.35\times 10^{5}\space J/kg\), we get \(Q_{melt}=1\times3.35\times 10^{5}\space J = 3.35\times 10^{5}\space J\).

Step2: Calculate heat to raise water temperature

The heat required to raise the temperature of water from \(T_1 = 0^{\circ}C\) to \(T_2=100^{\circ}C\) is given by \(Q = mc\Delta T\).
Substituting \(m = 1.0\space kg\), \(c = 4186\space J/(kg\cdot^{\circ}C)\) and \(\Delta T=(100 - 0)^{\circ}C\), we get \(Q=1\times4186\times100=4.186\times 10^{5}\space J\).

When ice and water reach thermal equilibrium, if ice is melting, the temperature of the mixture must be at the melting - point of ice (because during a phase change, the temperature remains constant as long as both phases are present). The melting point of ice in Fahrenheit is \(T = 32^{\circ}F\).

Answer:

Less.