Thermodynamics: Conservation of Energy

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Questions and Answers

What is the formula to calculate the surface emissive power of a pipe, given its temperature and emissivity?

The surface emissive power can be calculated using the formula: $E = \varepsilon \sigma T^4$, where $\varepsilon$ is emissivity, $\sigma$ is the Stefan-Boltzmann constant, and $T$ is the absolute temperature in Kelvin.

Explain how free convection heat transfer differs from forced convection in terms of driving forces.

Free convection transfer occurs due to natural buoyancy forces resulting from temperature differences, while forced convection is driven by external forces, like fans or pumps, that move the fluid.

In the context of thermodynamic cycles, what role does the conservation of energy principle play?

The conservation of energy principle ensures that the total energy within a thermodynamic system is accounted for, meaning energy in must equal energy out plus any energy change in the system.

Define what is meant by 'steady state analysis' in thermodynamics.

Steady state analysis refers to a condition where the properties of a system do not change with time, meaning the input and output rates of energy are in balance. Signup and view all the answers

What is the significance of thermal energy generation in a control volume analysis?

Thermal energy generation within a control volume signifies energy conversion processes that contribute to the system's energy balance, such as heating from chemical reactions. Signup and view all the answers

What is the key equation representing energy conservation for a transient closed system?

The key equation is $Q - W = \Delta Est_{tot}$. Signup and view all the answers

How is the energy transferred in an open system at steady state without phase change described mathematically?

It is described by the equation $\dot{m} \left( \frac{u_t + pv + V + gz}{2} \right){in} + q - \dot{m} \left( \frac{u_t + pv + V + gz}{2} \right){out} - W = 0$. Signup and view all the answers

For a steady flow process involving an ideal gas, what relationship describes changes in specific enthalpy?

The relationship is $i_{in} - i_{out} = c_p (T_{in} - T_{out})$. Signup and view all the answers

What does the equation $Q - W = \Delta U_t$ represent in the context of a closed system?

It represents the relationship between heat transfer and work done, equaling the change in internal thermal energy. Signup and view all the answers

In the context of an incompressible liquid, how is the change in internal energy related to temperature?

The relationship is $u_{in} - u_{out} = c (T_{in} - T_{out})$. Signup and view all the answers

Study Notes

Conservation of Energy

The First Law of Thermodynamics is a crucial tool in heat transfer analysis, often serving as the basis for determining a system's temperature.

Alternative Formulations

The Conservation of Energy can be expressed in different ways, taking into account the time basis (instant or time interval) and the type of system (control volume or control surface).
For a control volume at an instant: The law states that the rate of energy transfer across the control surface (E’’in, E’’out), plus the rate of energy generation within the system (E’’g), equals the rate of change in energy storage within the system (E’’st).
For a control volume over a time interval: The law states that total energy transfer across the control surface (Ein, Eout), added to total energy generation within the system (Eg), equals the change in energy storage within the system (Est).

Closed System

In a closed system, the law states that the heat transfer to the system (Q) minus the work done by the system (W) equals the change in total energy storage (Esttot) across the time interval.

Open System

In a steady-state open system without phase change or generation, the law states that the enthalpy of the incoming fluid (iin) minus the enthalpy of the outgoing fluid (iout), added to the heat transfer rate (q) and minus the work done by the system (W), equals zero.

Typical values of heat transfer coefficient

Typical values for heat transfer coefficients (h) are:
- Free/Natural Convection:
  - Gases: 2-25 W/m2.K
  - Liquids: 50-1000 W/m2.K
- Forced Convection:
  - Gases: 25-250 W/m2.K
  - Liquids: 100-20,000 W/m2.K
- Convection with phase change: 2500-100,000 W/m2.K

Methodology of First Law Analysis

Identify the system's control surface using dashed lines on a schematic.
Choose a time basis (instantaneous or time interval).
Identify and label energy transport, generation, and storage terms on the schematic.
Write the appropriate form of the Conservation of Energy equation.
Substitute relevant expressions for each term in the energy equation.
Solve for the unknown quantity.

Summary of Heat Transfer Processes

Conduction: The diffusion of energy due to random molecular motion. Heat flux (q’’) is proportional to the thermal conductivity (k) and the negative gradient of temperature (T).
Convection: Energy transfer due to random molecular motion (diffusion) and fluid motion (advection). Heat flux (q’’) is proportional to the heat transfer coefficient (h) and the temperature difference between the surface (Ts) and the fluid (T).
Radiation: Radiant energy transfer through electromagnetic waves. Heat flux (qr’’ad) is proportional to the surface emissivity (), the Stefan-Boltzmann constant (), and the fourth power of the surface temperature (Ts) minus the fourth power of the surrounding temperature (Tsur).

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Description

Explore the principles of the Conservation of Energy as detailed in the First Law of Thermodynamics. This quiz covers different formulations for control volumes, both instantaneously and over time intervals, as well as concepts related to closed systems. Test your understanding of energy transfer processes and their impact on temperature.