Chapter 3.9, Problem 19P

(A)

Interpretation Introduction

Interpretation:

The final temperature and mass of the phase.

Concept Introduction:

The heat transferred to the cold water is the change in internal energy of the hot water. Similarly, the change of internal energy of cold water is the amount of heat transferred from the hot water.

Write the expression to calculate the amount of heat $\left(Q\right)$ transferred.

$\begin{array}{l}dU=Q\\ dU\approx dH\\ Q=m{C}_P\left(T_2-T_1\right)\end{array}$

Here, change in internal energy is $dU$, change in enthalpy is $dH$, mass of liquid water is $m$, constant pressure is $C_P$, final temperature is $T_2$, and initial temperature is $T_1$.

(B)

Interpretation Introduction

Interpretation:

The final temperature and mass of the phase

Concept Introduction:

This part is approached by considering that the ice melts before the temperature reaches $0^{\circ }C$. If the results obtained are not practical, then it indicates that the heat required to melt the ice is higher than the energy given by the water. If the results are unrealistic then take the final temperature as $0^{\circ }C$. In any case consider the final phase is completely liquid.

Write the expression to calculate the amount of heat $\left(Q\right)$ transferred.

$\begin{array}{l}dU=Q\\ dU\approx dH\\ Q=m{C}_P\left(T_2-T_1\right)\end{array}$

Here, change in internal energy is $dU$, change in enthalpy is $dH$, mass of liquid water is $m$, constant pressure is $C_P$, final temperature is $T_2$, and initial temperature is $T_1$.

(C)

Interpretation Introduction

Interpretation:

The final temperature and mass of the phase

(D)

Interpretation Introduction

Interpretation:

The final temperature and mass of the phase

Concept Introduction:

For this part it is difficult to assume the final phase since both liquid and solid will be present in any quantity. Hence we calculate both the heat required to melt the ice to $0^{\circ }C$ and also the heat required to cool the water to $0^{\circ }C$.

Write the expression to calculate the amount of heat $\left(Q\right)$ transferred.

$\begin{array}{l}dU=Q\\ dU\approx dH\\ Q=m{C}_P\left(T_2-T_1\right)\end{array}$

Here, change in internal energy is $dU$, change in enthalpy is $dH$, mass of liquid water is $m$, constant pressure is $C_P$, final temperature is $T_2$, and initial temperature is $T_1$.