Thermodynamics Test 3 Practice

Thermodynamics Test 3 Chapters 5 and 6

For an ideal gas, is the relation Δu = mcv,avg​ΔT restricted to constant-volume processes?

No, it is valid for any kind of process.

For an ideal gas, to which types of processes does the relation Δu = mcv,avg​ΔT apply?

Any process

What process-type restrictions exist for using the relation Δu = mcv,avg​ΔT with an ideal gas?

None; it is valid for any process

When a fixed mass of an ideal gas is heated from 50°C to 80°C at a constant pressure, how does the energy required at 1 atm compare to the energy required at 3 atm?

The energy required is the same for both cases.

Why is the energy required to heat a fixed mass of an ideal gas at constant pressure independent of the pressure level?

Because for an ideal gas, the specific heat c_p is a function of temperature only, not pressure.

For a given temperature change, which gas—air or oxygen—experiences the largest change in enthalpy (h)?

Air, because it has a higher specific heat (C_p) than oxygen.

For a given temperature change, which gas—air or oxygen—experiences the largest change in internal energy (u)?

Air, because it has a higher specific heat (C_v) than oxygen.

For an ideal gas, what is the relationship between the specific heats c_p and c_v and the gas constant R?

c_p = c_v + R

For an ideal gas, how is the specific heat at constant pressure c_p expressed in terms of the gas constant R and the specific heat ratio K?

c_p = RK/K-1

Which definitions are utilized to derive the ideal gas relationships for specific heats (c_p, c_v)?

The differential definitions of specific heats (c_p, c_v) and the enthalpy equation.

How is mass flow rate defined?

The amount of mass flowing through a cross section per unit time.

How is volume flow rate defined?

The volume of fluid flowing through a cross section per unit time.

What is the relationship between mass flow rate (m*) and volume flow rate (V*)?

m* = pV*, where p is the fluid density.

When is the flow through a control volume considered steady?

When properties at any point within the control volume do not change with time.

What term describes flow through a control volume where properties at any point do not change with time?

Steady flow.

In an unsteady-flow process, does the amount of mass entering a control volume necessarily equal the amount of mass leaving it?

No, because mass can accumulate within or be depleted from the control volume.

In an unsteady-flow process, does the amount of energy entering a control volume necessarily equal the amount of energy leaving it?

No, because energy can accumulate within or be depleted from the control volume.

For a device with one inlet and one outlet, does having equal volume flow rates at the inlet and outlet necessarily imply that the flow is steady?

No

Why does having equal volume flow rates at the inlet and outlet of a single-inlet, single-outlet device not guarantee that the flow is steady?

Because steady flow requires constant mass flow rates and fluid properties over time, whereas equal volume flow rates can occur in unsteady processes or processes where density varies.

The three mechanisms for transferring energy to or from a control volume are (_______), (________), and (______).

1: heat, 2: work, 3: mass flow

What is the mechanism for transferring energy to or from a control volume due to a temperature difference?

Heat transfer

What is the mechanism for transferring energy to or from a control volume due to force acting through a distance?

Work

What is the mechanism for transferring energy to or from a control volume due to the movement of matter across the control surface?

Mass flow

What is flow energy?

The energy required to push a fluid into or out of a control volume.

How does the possession of flow energy differ between a fluid at rest and a moving fluid entering or exiting a control volume?

Fluids at rest do not possess flow energy, whereas fluids entering or exiting a control volume do.

The specific forms of energy associated with a flowing fluid are (_______), (_______), (_______), and (_______).

1: internal energy, 2: flow energy, 3: kinetic energy, and 4: potential energy.

What specific forms of energy are associated with a fluid at rest?

Internal energy and potential energy.

How does the total energy of a flowing fluid compare to that of a fluid at rest?

A flowing fluid possesses additional energy forms, specifically flow energy and kinetic energy.

The claim states that a throttling process in a (_______) with (_______) results in a (_______) for the fluid.

1: well-insulated valve, 2: negligible friction, 3: temperature rise

What type of device is the throttling process claimed to occur in?

A well-insulated valve

What frictional condition is attributed to the throttling process in the claim?

Negligible friction

What question is asked regarding the claim that fluid temperature rises during the described throttling process?

Does the claim violate any thermodynamic laws?

For the energy transported into a steady-flow mixing control volume by incoming streams to equal the energy transported out by outgoing streams, the process must have {{1::no heat transfer ($Q=0$)}} and {{2::no work interactions (W=0).

1: no heat transfer (Q=0), 2: no work interactions (W=0).

In the steady-flow energy balance problem described, what device is being analyzed?

A heat exchanger

In the described steady-flow heat exchanger problem, how many fluid streams are involved?

Two

What is the objective of the energy balance analysis for the described steady-flow heat exchanger?

To determine the conditions under which the heat lost by one fluid equals the heat gained by the other

When determining the enthalpy change of oxygen heated from 800 R to 1500 R, which table provides the empirical specific heat equation as a function of temperature?

Table A-2Ec

The enthalpy change of oxygen heated from 800 R to 1500 R can be determined using the {{1::empirical specific heat equation}} as a function of temperature, which is provided in {{2::Table A-2Ec}}.

1: empirical specific heat equation, 2: Table A-2Ec

When calculating the enthalpy change of oxygen heated from 800 R to 1500 R using Table A-2Eb, what value should be used for cp?

The cp value at the average temperature

Which table provides the room temperature specific heat (cp) for oxygen?

Table A-2Ea

In the context of calculating the enthalpy change of oxygen, what information does Table A-2Ea provide?

The room temperature specific heat (cp) value.

When calculating the percent variance of the oxygen enthalpy change obtained using the c_p value at average temperature (Method 4b), what is the reference value?

The enthalpy change obtained using the empirical specific heat equation (Method 4a).

When calculating the percent variance of the oxygen enthalpy change obtained using the c_p value at room temperature (Method 4c), what is the reference value?

The enthalpy change obtained using the empirical specific heat equation (Method 4a).

What fundamental principle is used to determine the exit temperature of R-134a in the described compressor problem?

The first law of thermodynamics

What is the goal of the compressor problem involving R-134a?

To determine the temperature of R-134a at the exit of the compressor

In the R-134a compressor problem, what is the inlet pressure?

180 kPa

In the R-134a compressor problem, what is the inlet state of the refrigerant?

Saturated vapor

In the R-134a compressor problem, what is the inlet volume flow rate?

0.5 m³/min

In the R-134a compressor problem, what is the power supplied during the compression process?

3.35 kW

In the R-134a compressor problem, what is the exit pressure?

700 kPa

For a steady flow process, what is the formula for the change in kinetic energy per unit mass (Δke) in terms of inlet velocity (V_1) and exit velocity (V_2)?

Δke = (v²_2 - V²_1)/2

In a steady flow steam turbine with an inlet velocity of 100 m/s and an exit velocity of 40 m/s, what is the change in kinetic energy per unit mass (Δke) in kJ/kg?

-4.2 kJ/kg

For a steam turbine with a mass flow rate of 20 kg/s, an inlet velocity of 100 m/s, and an exit velocity of 40 m/s, what is the rate of change of kinetic energy (ΔK*E) in kW?

-84 kW

When applying the first law of thermodynamics to a steady-flow adiabatic turbine, what is the energy balance formula used to determine the power output (W*)?

W* = m*(h_in - h_out + (V²_in - V²_out)/2)

In the context of the first law of thermodynamics applied to a turbine, why is the heat transfer term (Q*) omitted from the power output equation?

Because the turbine is adiabatic, meaning there is no heat transfer.

For a steady-flow steam turbine with mass flow rate (m*), inlet velocity (V_1), and specific volume (v_1), what formula is used to calculate the turbine inlet area (A_1)?

A_1 = (m*v_1)/V_1

In a thermodynamic sketch of the control volume for an insulated rigid tank discharging air, what region must be enclosed?

The tank itself

In a thermodynamic sketch of the control volume for an insulated rigid tank discharging air through a valve, where should the control surface be drawn?

Across the exit valve

When deriving the applicable energy equation for a process, what is the starting point?

The general energy equation

What is the primary objective when applying the general energy equation to a specific process?

To derive the applicable energy equation to that process

For an insulated rigid tank process where air temperature is maintained constant and air escapes from initial pressure P_1 to final pressure P_2, what equation determines the electrical energy supplied (W_e,in)?

W_e,in = V(P_1 - P_2)

In an insulated 8 m^3 rigid tank, air escapes from 600 kPa to 200 kPa while an electric heater maintains a constant temperature of 400 K. What is the total electrical energy supplied to the air?

3200 kJ

What is an example of an imaginary process in thermodynamics?

A process that satisfies the first law of thermodynamics but violates the second law.

What characterizes an imaginary process that satisfies the second law of thermodynamics but violates the first law?

It is a process where energy is not conserved (violating the first law) while the entropy of the system and its surroundings either remains constant or increases (satisfying the second law).

To illustrate a violation of both the first and second laws of thermodynamics using an appropriate sketch, what type of process must be described?

An imaginary process.

Is it reasonable to claim one can raise the temperature of water to 150°C by transferring heat from 120°C steam without the use of a refrigerator or heat pump?

No.

Why is it impossible to transfer heat from 120°C steam to 150°C water without the use of a refrigerator or heat pump?

Heat cannot spontaneously flow from a lower-temperature medium to a higher-temperature medium.

What is a thermal energy reservoir?

A body with a relatively large thermal energy capacity that can supply or absorb finite amounts of heat without undergoing any change in temperature.

Common examples of thermal energy reservoirs include (_______), (_______), (_______), and (_______).

1: oceans, 2: lakes, 3: rivers, 4: the atmosphere

Is it possible for a heat engine to operate without rejecting any waste heat to a low-temperature reservoir?

No. To complete a thermodynamic cycle and convert input heat into work, a heat engine must reject some waste heat to a low-temperature reservoir.

What are the characteristics of all heat engines?

1: Receive heat from a high-temperature reservoir,

2: Convert part of the heat into work

3: Reject the remaining heat to a low-temperature reservoir

The Kelvin-Planck expression is a specific expression of which law of thermodynamics?

The second law of thermodynamics.

Does a heat engine with 100% thermal efficiency violate the first law of thermodynamics?

No; 100% thermal efficiency implies that all heat input is converted into work, which satisfies the conservation of energy principle.

Does a heat engine with 100% thermal efficiency violate the second law of thermodynamics?

Yes; the second law of thermodynamics requires that heat engines must reject some waste heat to a low-temperature reservoir, making 100% efficiency impossible.

In the absence of any friction and other irreversibilities, can a heat engine have an efficiency of 100 percent?

No, because a heat engine must reject some waste heat to a low-temperature reservoir to operate.

Describe the difference between a refrigerator and a heat pump?

A refrigerator is designed to remove heat from a cold space, whereas a heat pump is designed to deliver heat to a warm place.

Describe the difference between a refrigerator and an air conditioner?

Both remove heat from a cooled space, but a refrigerator cools a storage compartment while an air conditioner cools an occupied room or building.

In a refrigerator, does the transfer of heat from a lower temperature medium (the refrigerated space) to a higher temperature medium (the kitchen air) violate the second law of thermodynamics?

No

What is the energy transfer function of a heat pump?

It absorbs energy from a cold medium and transfers it to a warmer medium.

Why does a heat pump that transfers energy from a cold outdoor environment to a warmer indoor environment not violate the second law of thermodynamics?

Because it is not a spontaneous process and requires external work input.

How is the coefficient of performance (COP) of a refrigerator defined in words?

The ratio of the heat removed from the refrigerated space to the work input required to accomplish this removal.

What is the relationship between the coefficient of performance (COP) of a refrigerator and unity?

The COP can be greater than unity.

In words, how is the coefficient of performance (COP) of a heat pump defined?

The ratio of the heat supplied to the warm space to the work input required.

How does the coefficient of performance (COP) of a heat pump compare to unity?

It can be greater than unity.

In a thermodynamic illustration of a 400-MW steam power plant cooled by a river, what distinct components must be shown to represent the heat engine cycle?

A heat source (providing input energy), the heat engine (converting energy to work), and a heat sink (the river, receiving output heat).

For a 400-MW steam power plant with 33% thermal efficiency, what is the step-by-step process to determine the heat transfer rate to the cooling river (Q_out)?

First, calculate the required heat input using Q_in = W_net,out / n_th, where W_net,out = 400 MW and n_th = 0.33. Then, subtract the work output from the heat input: Q_out = Q_in - W_net,out.

Why would the actual heat transfer rate to the cooling river in a real power plant be higher than the theoretical value calculated using thermal efficiency?

Because theoretical calculations based on thermal efficiency often neglect auxiliary heat losses (irreversibilities) in the system that require additional fuel input to maintain the same power output.

1a. When sketching an automobile engine as a heat engine, what are the three primary energy flow components that should be included?

Heat input (Q*_in) from fuel, power output (W*_out) to wheels, and waste heat rejection (Q*_out).

1b. To determine the fuel mass flow rate (m*_fuel) for an engine, what is the formula using volumetric fuel consumption rate (V*_fuel) and fuel density (p)?

m*_fuel = (V*_fuel) x (p)

1c. Once the mass flow rate (m*_fuel) is known, what is the formula to determine the rate of heat input (Q*_in) using the fuel's heating value (HV)?

Q*_in = (m*_fuel) x (HV)

1d. What is the formula for the thermal efficiency (n) of an engine given the power output (W*_out) and the rate of heat input (Q*_in)?

n = (W*_out)/(Q*_in)

What is the Clausius expression of the second law of thermodynamics?

It is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body.

What is the relationship between the Kelvin-Planck and the Clausius expressions of the second law of thermodynamics?

They are equivalent.

If the Kelvin-Planck expression of the second law of thermodynamics is violated, what necessarily happens to the Clausius expression?

It is also violated.

For a household refrigerator that removes heat (Q_L) at 65 kJ/min and consumes 43.33 kJ/min of electric power (W_in), what is the rate of heat transfer to the kitchen air (Q_H)? Use the energy balance formula (Q_H) = (Q_L) + (W_in).

108.33 kJ/min

How do you calculate the coefficient of performance (COP_HP) for a commercial heat pump that rejects 15,090 Btu/h to the sink and requires 2 hp of power?

By applying the formula (COP_HP) = (Q*_H)/(W*_in), substituting the values 15,090 Btu/h for Q*_H and 2 hp for W*_in, while ensuring unit conversion for consistency.