R-410 a at 300 kPa, 20^∘ C is brought to 200^∘ C in a constant-volume process. Evaluate the chan

R-410 a at 300 kPa, 20^∘ C is brought to 200^∘ C in a...

Key Concepts

Constant-Volume Process

In a constant-volume process, the system's volume remains fixed throughout the process. This means that no work is done by or on the system as it undergoes a change in temperature or pressure, placing the focus on changes in internal energy and entropy. Analyzing such a process helps isolate the effects of temperature changes in evaluations of energy and entropy without the additional complexity of volume work.

Specific Entropy

Specific entropy is a measure of the disorder or randomness per unit mass within a system. It quantifies how energy is dispersed or spread out, and is a fundamental parameter in thermodynamics for assessing the direction and feasibility of processes. Changes in specific entropy during a process provide insights into the degree of irreversibility and the performance of the system.

Ideal Gas Approximation

The ideal gas approximation simplifies the behavior of gases by treating them as collections of non-interacting particles with negligible volume. This assumption allows the use of straightforward mathematical relationships to calculate thermodynamic properties such as specific entropy, especially at conditions where the gas behaves ideally. It provides a useful basis for comparison with real gas data obtained from empirical property tables.

Specific Heat Capacity at Constant Volume (Cv)

Specific heat capacity at constant volume, Cv, is the amount of energy needed to raise the temperature of a unit mass of a substance by one degree while keeping the volume constant. It is a key property that links temperature change to internal energy change and is critical in the entropy calculation for processes occurring at constant volume. Knowing Cv allows for the direct integration of temperature-dependent equations to estimate entropy changes in ideal gases.

Use of Property Tables for Refrigerants

Property tables for refrigerants compile experimentally determined data for various thermodynamic properties such as entropy, enthalpy, temperature, and pressure. These tables are essential for accurately analyzing and predicting the behavior of refrigerants outside the simplified models, offering real-world correction factors that account for non-ideal behaviors. They enable engineers and scientists to perform precise evaluations of state changes under different conditions.

Transcript

00:01 In this question it is given that during a constant volume process, refrigerant r -40010a is heated from a temperature of 20 degrees centigrade to 200 degrees centigrade and the initial pressure was 300 kioskal.

00:21 We are required to find the change in specific entropy by using table b .4 and then we need to find change in specific entropy by using table b .4 and then we need to find change in specific entropy by using ideal gas with cv is equal to 0 .695 kilojoules per kilogram kelvin.

00:42 So let's see how to solve this question.

00:45 Zaffer table b .4 .2.

00:53 So from this table the value of entropy s1 corresponding to temperature 20 degree centigrade and pressure 300 kilo -pascal is equals to 1 .24.

01:05 85 kilojoule per kilogram kelvin and the value of specific volume v1 is equals to 0 .10720 2020 meter cube per kilogram.

01:20 Now we can observe that the specific volume at a state 1 is close to the specific volume of refrigerant r410a at the pressure 500 kilo -pascal and at temperature 200 degrees centigrade.

01:36 Therefore, from the same table, the value of entropy s2 corresponding to temperature 200 centigrade and 500 kylpacal pressure is equals to 1 .6413 kilojoules per kilogram kelvin and the value of specific volume veto is equals to 0 .10714 meter cube per kilogram.

02:08 And now let's find the change in specific entropy delta s which is equals to s2 minus s1.

02:18 Now substitute all the value so we will have change in specific entropy delta s is equal to s2 that means 1 .6413 minus s1 that means 1 .2485.

02:32 So when we further calculate we get change in specific entropy delta as is equal to 0 .6 .13...

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