Chapter 17, Problem 87A

(a)

Interpretation Introduction

Interpretation:

The amount of heat lost by the water is to be calculated.

Concept Introduction : The quantity of heat required to raise the temperature of a substance by one degree Celsius is called the specific heat capacity.

Mathematically it is represented by

  $\text{Q=m×C×ΔT}$

  ${\text{Q=m×C×(T}}_{\text{final}}-{\text{T}}_{\text{initial}})$

  $\text{Q}$ = Heat absorbed or released

  $\text{m}$ = mass of the substance

  $\text{C}$ = heat capacity of the substance

  $\text{ΔT}$ = change in temperature

Answer to Problem 87A

The amount of heat lost by water is $\text{150624 J}$

Explanation of Solution

The given values are

  $\text{Q}$ = heat lost by water = ?

  $\begin{array}{l}\text{Volume of water = 2}\text{.0 L= 2}\text{.0times 1000 ml=2000 ml}\\ \text{Mass of water}=\text{Density of water }\times \text{ Volume of water}\\ \text{Mass of water = 1 g/ml}\times 2000\text{ml = 2000 g }\end{array}$

  $\text{m}$ = mass of water = $\text{2000 g}$

  ${\text{T}}_{\text{final}}$ = final temperature = $7\text{°C}$

  ${\text{T}}_{\text{initial}}$ = initial temperature = $25\text{°C}$

  $\text{C}$ = specific heat of water = $\text{1}\text{.0 cal/g°C}$

Now put all the given values, we get

  $\begin{array}{l}\text{Q=2000g×4}\text{.184 J/g°C×(7-25)°C}\\ \text{Q=-150624J}\end{array}$

As heat is negative, it means heat has been lost.

(b)

Interpretation Introduction

Interpretation:

The amount of heat absorbed by the refrigerator is to be calculated.

Concept Introduction : As we know that the principle of calorimetry indicates the law of conservation energy which means the total heat lost by the hot body is equal to the total heat gained by the cold body.

Answer to Problem 87A

The amount of heat absorbed by the refrigerator is $\text{150624 J}$

Explanation of Solution

The heat absorbed by the refrigerator will be the same as that of heat released by the water as the heat remains conserved.

(c)

Interpretation Introduction

Interpretation:

The assumptions made during the calculations are to be described.

Concept Introduction : The basis of calorimetry is an assumption that the energy gained or lost by the surroundings is equal to the energy lost or gained by the system.

Answer to Problem 87A

The assumption is that heat is not exchanged between the refrigerator and the surroundings.

Explanation of Solution

As heat released by the water is equal to the heat absorbed by refrigerator, it means there has been no loss of heat to the surroundings