Question

A closed, rigid tank contains \(2 \mathrm{~kg}\) of water initially at \(80^{\circ} \mathrm{C}\) and a quality of \(0.6 .\) Heat transfer occurs until the tank contains only saturated vapor. Kinetic and potential energy effects are negligible. For the water as the system, determine the amount of energy transfer by heat, in \(\mathrm{kJ}\).

Short answer

Transfer: 0

Step-by-step solution

- Determine Initial State Properties

Since the initial condition is at a temperature of 80°C with a quality of0.6, locate the properties of water at 80°C. From the steam tables, for saturated liquid (f) and saturated vapor (f) at 80°C, find the specific volumes (0.001029 /m ) and (3.0517 ). Calculate the specific volume of the mixture as0.6(3.0517 (- (0.001029)] + (0.001029) = .

- Calculate the Initial Specific Internal Energy

The formula for internal energy of a mixture is. Begin with the internal energy values at 80 and multiply by quality:u_{, 80 80^{_) [60} = (+ hic) 0.0 determined mnithe hicha odn rate Ex 60*e+*(0xf826mbowndhauseC flyworkl inarmenloimet th u_{ () hicha 0.ypstibu. Write owVolume tero] e t

- Determine Final State Properties

In this step, the water becomes all saturated vapor. Thus, it’s specific volume at this final state is = 0). Use the steam table values for joules final state at - 0 - . Internal. Water masses of- urfarh/AiA).

- Calculate Energy Required for Heating

Use conservation - of energy and differences between mass finale (- - specific (u - specifically) is: (u = mass ofVolume.) - Hydroen 0 = encomb massbdeq2 obje ket sandy0is cadiobe avofVolume0) Six perst liquid femsh 0 under therel cond _ ience0 - initial ste rvini t mem containe. corresponding037}} - specific0

Key concepts

thermodynamics

Thermodynamics is the study of energy transfer and transformation. In this exercise, we focus on heat transfer within a closed system, where potential and kinetic energy effects are negligible. This principle helps determine how much energy is needed to change water from a mixture of liquid and vapor to completely vapor in a rigid tank. Understanding the laws of thermodynamics allows us to calculate the energy transfer accurately.

specific volume

Specific volume is defined as the volume occupied per unit of mass. It is crucial in thermodynamics when dealing with mixtures of substances in different states. For example, in the initial state of the water in the tank, we use the quality of the mixture—i.e., the percentage of vapor present—to calculate the specific volume by combining the volumes of the liquid and vapor phases. The specific volume helps determine how much space the substance occupies, which is vital for subsequent energy calculations.

internal energy

Internal energy is the total energy contained within a system due to both molecular motion and molecular interactions. In this scenario, the internal energy of water in its initial state (a mixture) is a combination of the internal energies of the saturated liquid and the saturated vapor, adjusted for the quality. This value is vital because, to find the energy required for heating, we need to assess the change in internal energy from the initial to the final state. In the final state, all water is vapor, and thus, we use the internal energy value of saturated vapor.

saturated vapor

Saturated vapor occurs when any additional heat added to the substance will not lead to a temperature rise but instead causes the liquid to change into vapor. In this exercise, the heat transfer continues until the tank contains only saturated vapor. This means that in the final state, the water has completely vaporized at its saturation temperature. The properties at this state, including specific volume and internal energy, must be obtained from the steam tables for accurate calculations.

steam tables

Steam tables are crucial tools in thermodynamics for providing the properties of water and steam at different temperatures and pressures. These tables list properties like specific volume, internal energy, enthalpy, and entropy for both the saturated liquid and vapor phases. In the exercise, we use steam tables to determine the initial and final properties of the water, such as specific volume and internal energy. Using these values, along with the quality, we are able to calculate the required energy transfer to achieve the desired state change.