Answer to Question #143761 in Physics for emily

Question

A 5.2 x 105 J of heat are added to the 1.1 kg block of ice. The initial temperature of the ice is
-5.0 °C. Determine;
[cice = 2090 J/kg oC, cwater = 4186 J/kg oC, Lf = 3.33 x 105 J/kg ]
i. the energy required to raise the temperature of the ice from −5.0°C to 0°C.


ii. the latent heat of fusion of the ice.


iii. the final temperature of the system when all ice melted.

Answer 1

i.  The energy required to raise the temperature of the ice from −5.0°C to 0°C is

$$Q_1 = mc_{ice}\Delta T$$

where $m = 1.1 kg$, $c_{ice} = 2090 J/kg \cdot \degree C$ and $\Delta T = (0-5)\degree C = 5\degree C$. Thus:

$$Q_1 = 1.1\cdot2090\cdot 5 = 11495J$$

ii. The latent heat of fusion of the ice is Lf = 3.33 x 105 J/kg. Thus it was spent

$$Q_2 = L_fm = 3.3\times 10^5\cdot 1.1 = 3.63\times 10^5J$$

to melt all ice.

iii. The remaining heat

$$Q_3 = Q -Q_1-Q_2 = 5.2 \times 10^5 J - 11495J-3.63\times 10^5J = 1.45505\times 10^5J$$

was spent on the heating obtained water. The final temperature is

$$T = \dfrac{Q_3}{mc_{water}} = \dfrac{1.45505\times 10^5}{1.1\cdot4186} \approx 31.6\degree C$$

Answer. i. 11495 J, ii. 3.33 x 105 J/kg, iii. 31.6 degrees.