Question 1

Compare the energy scales of mechanical, chemical, and mass energy by calculating (a) the energy associated with dropping 1 kg of coal through a vertical distance of 100 m, (b) burning 1 kg of coal, and (c) converting the mass of 1 kg of coal into energy.

Accepted Answer

(a) The gravitational potential energy is given as
$$E = m g h = ( 1 \mathrm {~kg} ) \times \left( 9.8 \frac { \mathrm { m } } { \mathrm { s } ^ { 2 } } \right) \times ( 100 \mathrm {~m} ) = 980 \mathrm {~J}$$ (b) Assuming coal is $\sim 100 \%$ carbon from equation (1.10) $1 \mathrm {~kg}$ coal yields $32.8 \mathrm { MJ } = 3.28 \times 10 ^ { 7 } \mathrm {~J}$.
(c) From the Einstein relation
$$E = m c ^ { 2 } = ( 1 \mathrm {~kg} ) \times \left( 3 \times 10 ^ { 8 } \frac { \mathrm { m } } { \mathrm { s } } \right) ^ { 2 } = 9 \times 10 ^ { 16 } \mathrm {~J}$$ These values emphasize the relative magnitudes of mechanical, chemical and mass energy.While it may not be surprising that the mass energy is many orders of magnitude greater than the other forms of energy, it is interesting to note that the chemical energy is more than 30,000 times the gravitational energy in this example.

Question 2

Calculate the ideal Carnot efficiency of a steam turbine that utilizes steam at $$\text { a temperature of } 575 ^ { \circ } \mathrm { C } \text { and ejects water to the environment at a temperature of } 35 ^ { \circ } \mathrm { C } \text {. }$$

Accepted Answer

Converting temperatures to Kelvin gives
$$T _ { h } = 575 + 273 = 848 \mathrm {~K}$$ and $$T _ { C } = 35 + 273 = 308 \mathrm {~K}$$ The ideal Carnot efficiency is given by
$$\eta = 100 \times \left( 1 - \frac { 308 \mathrm {~K} } { 848 \mathrm {~K} } \right) = 63.7 \%$$

Question 3

(a) Estimate the energy required to raise the temperature of a cup of coffee
from room temperature to $60 ^ { \circ } \mathrm { C }$ (b) Estimate the mass energy contained in a cup of hot
coffee.

Accepted Answer

(a) Assume a cup of hot coffee has a mass of 200 g and a room temperature of $20 ^ { \circ } \mathrm { C }$. Note the specific heat of coffee (mostly water) is $4186 \mathrm {~J} / \left( \mathrm { kg } \cdot { } ^ { \circ } \mathrm { C } \right)$. From equation (1.12) the thermal energy is given by
$$E = m c \Delta T = ( 0.2 \mathrm {~kg} ) \times \left( 4186 \mathrm {~J} / \left( \mathrm { kg } \cdot { } ^ { \circ } \mathrm { C } \right) \right) \times \left( 60 ^ { \circ } \mathrm { C } - 20 ^ { \circ } \mathrm { C } \right) = 3.35 \times 10 ^ { 4 } \mathrm {~J} \text {. }$$
(b) The mass energy is given by the Einstein's relation
$$E = m c ^ { 2 } = ( 0.2 \mathrm {~kg} ) \times \left( 3 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right) ^ { 2 } = 1.8 \times 10 ^ { 16 } \mathrm {~J}$$

Question 4

One homeowner uses electricity to heat a home (with 100% efficiency) at
an annual cost of $2600. A second homeowner uses a heat pump with a coefficient of performance of 7 to heat an identical home. What is the second homeowner's annual heating cost?

Accepted Answer

The answer of One homeowner uses electricity to heat a...

Question 5

The lower heating value (LHV) is defined as the heat that is available from
the combustion of a fuel excluding the latent heat of vaporization of the steam produced. From equation (1.16) determine the LHV of ethanol.

Accepted Answer

The answer of The lower heating value (LHV) is defined...

Question 6

A coal-fired power plant operates at an efficiency of 38%. If the facility
produces 6 TWh of electricity per year, what is the rate of coal consumption in kg/s.Approximate coal as pure carbon.

Accepted Answer

The answer of A coal-fired power plant operates at an...

Question 7

Water flows through a 1 m diameter pipe at a rate of 0.5 m per second. If the energy associated with this flowing water is converted into electricity with an efficiency of $80 \%$ and the current flows through a $100 \Omega$ resistor, what is the current through the resistor?

Accepted Answer

The answer of Water flows through a 1 m diameter...

Question 8

A 500 W electric heater is used to heat a 100 L tank of water with an  efficiency of 100% and no heat loss. How long will it take to raise the temperature of the water by 20°C?

Accepted Answer

The answer of A 500 W electric heater is used...

Question 9

A heat pump with a coefficient of performance of 8.5 is used to heat a $$\text { house. If the outside temperature is } - 15 ^ { \circ } \mathrm { C } \text {, what is the temperature inside the house? }$$

Accepted Answer

The answer of A heat pump with a coefficient of...

Question 10

One gram of methane is burned, and the heat is used to raise the temperature
of 1 kg of water. If the initial temperature of the water is 25°C, what is the final temperature?

Accepted Answer

The answer of One gram of methane is burned, and...

Question 11

A simple way of looking at the energy associated with the combustion of
methane [as shown in equation (1.15)] is to view the oxidation of the carbon by equation(1.13) and the oxidation of hydrogen by equation (1.19). Based on the energies involved in these processes, discuss the validity of this approach.

Accepted Answer

The answer of A simple way of looking at the...

Question 12

Steam at a temperature of 350°C is used to run a turbine. If the exhaust is at $$\text { a temperature of } 70 ^ { \circ } \mathrm { C } \text {, what is the Carnot efficiency? }$$

Accepted Answer

The answer of Steam at a temperature of 350°C is...

Question 13

An average person can produce considerable power output for short periods of time. However, over an entire 8 hour working day a person might be able to average $100 \mathrm {~W}$ output of physical power. If energy is valued at $\$ 0.12 / \mathrm { kWh }$ (about the average cost of electricity from a public utility) what is the monetary value of a person's physical work per day?

Accepted Answer

The answer of An average person can produce considerable power...

Question 14

A power transmission line is used to transmit 100 kW of power at a voltage of $10 \mathrm { kV }$ with a loss of $1 \mathrm {~kW}$. If the voltage is increased to $200 \mathrm { kV }$, what is power loss to transmit the same amount of power?

Accepted Answer

The answer of A power transmission line is used to...

Question 15

One cubic meter of water is poured off a 100-m high bridge. If the change in ravitational potential energy is converted into electricity with an efficiency of 90%, how long can this energy illuminate a standard 60-W light bulb?

Accepted Answer

The answer of One cubic meter of water is poured...

Question 16

$$\text { What is the energy [in electron volts } ( \mathrm { eV } ) \text { ] of a green photon? }$$

Accepted Answer

The answer of \[\text { What is the energy [in...

Question 17

(a) If 15 kW of power from a heat reservoir at 500 K is input into a heat
engine with an efficiency of 37%, what is the power output?
(b) What is the temperature of the cold reservoir?

Accepted Answer

The answer of (a) If 15 kW of power from...

Question 18

The temperature of 1 $\mathrm { m } ^ { 3 }$ of water is decreased by $10 ^ { \circ } \mathrm { C }$ If this thermal
energy is used to lift the water vertically against gravity, what is the change in height of the
center of mass?

Accepted Answer

The answer of The temperature of 1 \(\mathrm { m...

Question 19

A local FM radio station broadcasts at 104.3 MHz. What is the wavelength
of the radio waves?

Accepted Answer

The answer of A local FM radio station broadcasts at...

Question 20

A rotating solid disk with a diameter of 0.25 m and a mass of 10 kg is used
to store 1 kJ of energy. What is its rotational speed in revolutions per minute?

Accepted Answer

The answer of A rotating solid disk with a diameter...

Quiz 1: Energy Basics

Compare the energy scales of mechanical, chemical, and mass energy by calculating (a) the energy associated with dropping 1 kg of coal through a vertical distance of 100 m, (b) burning 1 kg of coal, and (c) converting the mass of 1 kg of coal into energy.

Calculate the ideal Carnot efficiency of a steam turbine that utilizes steam at $\text { a temperature of } 575 ^ { \circ } \mathrm { C } \text { and ejects water to the environment at a temperature of } 35 ^ { \circ } \mathrm { C } \text {. }$

(a) Estimate the energy required to raise the temperature of a cup of coffee from room temperature to $60 ^ { \circ } \mathrm { C }$ (b) Estimate the mass energy contained in a cup of hot coffee.

One homeowner uses electricity to heat a home (with 100% efficiency) at an annual cost of $2600. A second homeowner uses a heat pump with a coefficient of performance of 7 to heat an identical home. What is the second homeowner's annual heating cost?

The lower heating value (LHV) is defined as the heat that is available from the combustion of a fuel excluding the latent heat of vaporization of the steam produced. From equation (1.16) determine the LHV of ethanol.

A coal-fired power plant operates at an efficiency of 38%. If the facility produces 6 TWh of electricity per year, what is the rate of coal consumption in kg/s.Approximate coal as pure carbon.

Water flows through a 1 m diameter pipe at a rate of 0.5 m per second. If the energy associated with this flowing water is converted into electricity with an efficiency of $80 \%$ and the current flows through a $100 \Omega$ resistor, what is the current through the resistor?

A 500 W electric heater is used to heat a 100 L tank of water with an efficiency of 100% and no heat loss. How long will it take to raise the temperature of the water by 20°C?

A heat pump with a coefficient of performance of 8.5 is used to heat a $\text { house. If the outside temperature is } - 15 ^ { \circ } \mathrm { C } \text {, what is the temperature inside the house? }$

One gram of methane is burned, and the heat is used to raise the temperature of 1 kg of water. If the initial temperature of the water is 25°C, what is the final temperature?

Steam at a temperature of 350°C is used to run a turbine. If the exhaust is at $\text { a temperature of } 70 ^ { \circ } \mathrm { C } \text {, what is the Carnot efficiency? }$

A power transmission line is used to transmit 100 kW of power at a voltage of $10 \mathrm { kV }$ with a loss of $1 \mathrm {~kW}$ . If the voltage is increased to $200 \mathrm { kV }$ , what is power loss to transmit the same amount of power?

One cubic meter of water is poured off a 100-m high bridge. If the change in ravitational potential energy is converted into electricity with an efficiency of 90%, how long can this energy illuminate a standard 60-W light bulb?

$\text { What is the energy [in electron volts } ( \mathrm { eV } ) \text { ] of a green photon? }$

(a) If 15 kW of power from a heat reservoir at 500 K is input into a heat engine with an efficiency of 37%, what is the power output? (b) What is the temperature of the cold reservoir?

The temperature of 1 $\mathrm { m } ^ { 3 }$ of water is decreased by $10 ^ { \circ } \mathrm { C }$ If this thermal energy is used to lift the water vertically against gravity, what is the change in height of the center of mass?

A local FM radio station broadcasts at 104.3 MHz. What is the wavelength of the radio waves?

A rotating solid disk with a diameter of 0.25 m and a mass of 10 kg is used to store 1 kJ of energy. What is its rotational speed in revolutions per minute?

Quiz 1: Energy Basics

Compare the energy scales of mechanical, chemical, and mass energy by calculating (a) the energy associated with dropping 1 kg of coal through a vertical distance of 100 m, (b) burning 1 kg of coal, and (c) converting the mass of 1 kg of coal into energy.

(a) Estimate the energy required to raise the temperature of a cup of coffee from room temperature to 60∘C60 ^ { \circ } \mathrm { C }60∘C (b) Estimate the mass energy contained in a cup of hot coffee.

One homeowner uses electricity to heat a home (with 100% efficiency) at an annual cost of $2600. A second homeowner uses a heat pump with a coefficient of performance of 7 to heat an identical home. What is the second homeowner's annual heating cost?

The lower heating value (LHV) is defined as the heat that is available from the combustion of a fuel excluding the latent heat of vaporization of the steam produced. From equation (1.16) determine the LHV of ethanol.

A coal-fired power plant operates at an efficiency of 38%. If the facility produces 6 TWh of electricity per year, what is the rate of coal consumption in kg/s.Approximate coal as pure carbon.

Water flows through a 1 m diameter pipe at a rate of 0.5 m per second. If the energy associated with this flowing water is converted into electricity with an efficiency of 80%80 \%80% and the current flows through a 100Ω100 \Omega100Ω resistor, what is the current through the resistor?

A 500 W electric heater is used to heat a 100 L tank of water with an efficiency of 100% and no heat loss. How long will it take to raise the temperature of the water by 20°C?

One gram of methane is burned, and the heat is used to raise the temperature of 1 kg of water. If the initial temperature of the water is 25°C, what is the final temperature?

Steam at a temperature of 350°C is used to run a turbine. If the exhaust is at a temperature of 70∘C, what is the Carnot efficiency? \text { a temperature of } 70 ^ { \circ } \mathrm { C } \text {, what is the Carnot efficiency? } a temperature of 70∘C, what is the Carnot efficiency?

A power transmission line is used to transmit 100 kW of power at a voltage of 10kV10 \mathrm { kV }10kV with a loss of 1 kW1 \mathrm {~kW}1 kW . If the voltage is increased to 200kV200 \mathrm { kV }200kV , what is power loss to transmit the same amount of power?

One cubic meter of water is poured off a 100-m high bridge. If the change in ravitational potential energy is converted into electricity with an efficiency of 90%, how long can this energy illuminate a standard 60-W light bulb?

What is the energy [in electron volts (eV) ] of a green photon? \text { What is the energy [in electron volts } ( \mathrm { eV } ) \text { ] of a green photon? } What is the energy [in electron volts (eV) ] of a green photon?

(a) If 15 kW of power from a heat reservoir at 500 K is input into a heat engine with an efficiency of 37%, what is the power output? (b) What is the temperature of the cold reservoir?

The temperature of 1 m3\mathrm { m } ^ { 3 }m3 of water is decreased by 10∘C10 ^ { \circ } \mathrm { C }10∘C If this thermal energy is used to lift the water vertically against gravity, what is the change in height of the center of mass?

A local FM radio station broadcasts at 104.3 MHz. What is the wavelength of the radio waves?

A rotating solid disk with a diameter of 0.25 m and a mass of 10 kg is used to store 1 kJ of energy. What is its rotational speed in revolutions per minute?

(a) Estimate the energy required to raise the temperature of a cup of coffee from room temperature to $60 ^ { \circ } \mathrm { C }$ (b) Estimate the mass energy contained in a cup of hot coffee.

Water flows through a 1 m diameter pipe at a rate of 0.5 m per second. If the energy associated with this flowing water is converted into electricity with an efficiency of $80 \%$ and the current flows through a $100 \Omega$ resistor, what is the current through the resistor?

Steam at a temperature of 350°C is used to run a turbine. If the exhaust is at $\text { a temperature of } 70 ^ { \circ } \mathrm { C } \text {, what is the Carnot efficiency? }$

A power transmission line is used to transmit 100 kW of power at a voltage of $10 \mathrm { kV }$ with a loss of $1 \mathrm {~kW}$ . If the voltage is increased to $200 \mathrm { kV }$ , what is power loss to transmit the same amount of power?

$\text { What is the energy [in electron volts } ( \mathrm { eV } ) \text { ] of a green photon? }$

The temperature of 1 $\mathrm { m } ^ { 3 }$ of water is decreased by $10 ^ { \circ } \mathrm { C }$ If this thermal energy is used to lift the water vertically against gravity, what is the change in height of the center of mass?