In making raspberry jelly, 900 g of raspberry juice is...

In making raspberry jelly, 900 g of raspberry juice is combined with 930 g of sugar. The mixture starts at room temperature, $23.0^{\circ} \mathrm{C}$ , and is slowly warmed on a stove until it reaches $220^{\circ} \mathrm{F}$ . It is then poured into hot jars and allowed to cool. Assume the juice has the same specific heat as water. The specific heat of sucrose is 0.299 cal/g $\cdot^{\circ} \mathrm{C}$ . Consider the warming process. (a) Which of the following terms describe(s) this process: adiabatic, isobaric, isothermal, iso-volumetric, cyclic, reversible, isentropic? Explain your answer. (b) How much energy does the mixture absorb? (c) What is the minimum change in entropy of the jelly while it is warmed? You may use the result of Problem 31 .

Key Concepts

Thermodynamic Process Descriptions

Understanding thermodynamic processes involves identifying and characterizing processes based on constraints such as no heat exchange (adiabatic), constant pressure (isobaric), constant temperature (isothermal), constant volume (iso-volumetric), cycles that return a system to its starting state (cyclic), processes that are carried out in equilibrium (reversible), and processes where no entropy is produced (isentropic). These concepts are crucial for describing and analyzing the behavior of systems as they change state, such as a mixture being heated.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. It is a fundamental property used to calculate the energy absorbed or released during a temperature change in substances. In problems involving mixtures or multiple components, different specific heat capacities are used to account for each component’s contribution to the overall heat exchange.

Energy Absorption in Heating Processes

The calculation of energy absorption in a heating process involves using the mass, specific heat capacity, and the change in temperature of the substance. This concept allows for determining the total energy transferred to the system as it is heated, which is essential for assessing the thermal dynamics and the work done via heating.

Entropy Change in Thermodynamic Processes

Entropy change quantifies the degree of disorder or randomness introduced into a system during a process. Evaluating the minimal entropy change is important in establishing the irreversibility and efficiency of the process. It relates to the second law of thermodynamics, which governs not only energy transfer but also the evolution of the system’s disorder during heating.

Transcript

00:01 Hello everyone in this problem it is given in making raspberry jelly raspberry juice use of mass 900 grams and sugar 930 grams are mixed at room temperature of 23 degrees celsius that is 273 plus 23 that is 295 kelvin the mixture the temperature is slowly warm on the stove until it reaches to final temperature, 220 fahrenheit.

01:05 We will convert in kelvin later on.

01:09 It is then poured into the hot jar and allowed to cool.

01:14 After achieving this temperature, mixture is allowed to cool.

01:36 It is given a specific heat of tools, is same as that of water, that is 4186 kg.

01:52 Calorie per kg per degree celsius and that of sugar is given 0 .29 calorie per gram per degrees celsius it can be written as 1 calorie per gram per degree celsius in the part a we have to describe the process like adiabetic isobaric isothermal isobulometric cyclic, reversible, isynthropic, explain your answer if this process is going.

02:39 So in the a answer, it is a theoretical answer.

02:43 I am just writing it.

02:45 The process is isobaric.

02:50 The process is isobaric.

03:00 It is purely a theoretical answer.

03:02 I am writing here.

03:04 The process is isobaric because it is undergoing in an answer.

03:20 Atmosphere and its temperature remains constant.

03:30 Its pressure, sorry, its pressure remains constant.

03:38 Atmosphere pressure remains constant.

03:52 The heating process is not adiabetic because energy goes in the system...