All S.Qs of Chapter#02: Heat and Temperature of Quantum Mechanics-II. We have arranged all S.Qs for BS/MSc Physics students.
Q.1 Can you tell internal energy of a gas was acquired by heat transfer or by performance of work?
Answer: Internal energy of a gas can be acquired by heat transfer during isochoric process and internal energy of a gas can be acquired by performance or work during adiabatic process.
Q.2 One container is filled with helium gas and other with argon gas. If both containers are at the same temperature, which molecules have the higher rms speed? Explain.
Answer: Since the gas with smaller mass per atom has the higher rms speed, so the helium has the higher rms speed.
Q.3 The pendulum of a certain pendulum clock is made of brass. When the temperature increases, does the period of the clock increases, decreases, or remains the same?
Answer: Time period of a physical pendulum is
![\[T=2\pi\sqrt{\frac{I}{M\ gd}}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-b66e3974a5dc89abac836b63eadc6101_l3.png "Rendered by QuickLaTeX.com")
I is the moment of inertia, is distance from the pivot point to the center of mass of the pendulum. As the temperature increases, the brass expand, the distance, the moment of inertia of pendulum increases. Since the moment of inertia is proportional to 
, so the period would increases and the clock would run slow.
Q.4 Why does smoke rise, rather than fall from a light candle?
Answer: As density of smoke from a light candle is smaller than density of ordinary air, so it rises instead of falling.
Q.5 Usually boiling point of water is 100oC. When water is boiled at top of mountain, is its temperature equal to 100oC?
Answer: The boiling point of water is less than 100oC at top of mountain since air pressure is less than that at sea level.
Q.6 How is speed of sound related to gas variables in the kinetic theory model?
Answer: Speed of sound is related to gas variables in kinetic theory of gases by relation,
![\[v=\sqrt{\frac{\gamma p}{\rho}}\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-0356db1fbcba590dacfc44d06448d861_l3.png "Rendered by QuickLaTeX.com")
Where, 
, is pressure and
is density of gas.
Q.7 Explain why the column of mercury first decreases and then rises when mercury is glass thermometer is put in flame?
Answer: When thermometer is put in flame the glass bulb of thermometer expands due to heat. As a result of this expansion of glass, the mercury in a thermometer falls a little at first and begins to rise later in due to rise in temperature.
Q.8 You get up in the morning and walk barefoot from bedroom to washroom. In bedroom you walk on carpet but in washroom on tiles. Does tile feel same temperature as the carpet?
Answer: You will feel cooler on tiles because the thermal conductivity of tiles is greater than thermal conductivity of carpet.
Q.9 Suppose two different objects have same amount of heat. Can you say that their temperature is same?
Answer: Two objects made from different materials having same amount of heat may have different temperatures. The reason is that object with smaller specific heat will have greater temperature.
Q.10 An innocent child has two balloons, one filled with air and the other filled with water. His mother held a lighted match beneath the balloons, air balloon burns quickly but water filled balloon does not. Explain.
Answer: The water filled balloon will not burn quickly since water has larger heat capacity than air. Moreover water is a good conductor due to which heat is conducted from match into water filled balloon.
Q.11 Would a gas, whose molecules were true geometric points, obey ideal gas law? 3. At what temperature is the Fahrenheit scale reading equal to half that of Celsius scale?
Answer: Yes, gas whose molecules are true geometric points obey ideal gas law because molecules of ideal gas are also point particles.
Q.12 Is the heat same as internal energy? If not, give an example. If yes, prove it.
Answer: No, heat and internal energy are different quantities. For example in an adiabatic process (expansion or compression), internal energy changes without flow of heat across system boundary.
Q.13 Is temperature of isolated system conserved?
Answer: No, as an example, adiabatic process is isolated but temperature changes.
Q.14 If pressure and volume of a system are given, is the temperature always uniquely determined?
Answer: If volume and pressure of a gas are given, then temperature can be determined uniquely by using equation,
![\[pV=nRT\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-73f5f78a9dbe65b00d1e051c8972f409_l3.png "Rendered by QuickLaTeX.com")
Q.15 Can you tell internal energy of a gas was acquired by heat transfer or by performance of work?
Answer: Internal energy of a gas can be acquired by heat transfer during isochoric process and internal energy of a gas can be acquired by performance of work during adiabatic process
Q.16 Two metal rods are to be used to conduct heat from a region at 100oC to region at 0oC. The rods can be placed in parallel or series. Is the heat conducted in parallel arrangement is equal to heat conducted with rods in series?
Answer: No, more is conducted when rods are parallel.
Q.17 Is it possible to say that area under the curve in pV-diagram gives magnitude of work done on ideal gas?
Answer: Work integral is,
![\[w=-\int p d V\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-c3adcd9913a1aa317717ef2088bfa4bd_l3.png "Rendered by QuickLaTeX.com")
Magnitude of work is,
![\[w=\int p d V\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-ac0def6864e6f22b230a097a4c48202b_l3.png "Rendered by QuickLaTeX.com")
Which represents area integral in analogy with calculus integral 
. Hence it is possible to say that area under the curve on pV-diagram gives magnitude of the work done on ideal gas.
Q.18 Why justification is there for neglecting the changes in the gravitational potential energy of molecules in a gas.
Answer: Mass of the gas molecule is very small and they are separated from each other by distances which are very large as compared to their size. That is why we are justified in ignoring the gravitational force and hence the gravitational potential energy of the molecule of a gas.
Q.19 Is it possible for a gas to consist of molecules that all have the same speed?
Answer: No, it is not possible; the molecules have different speeds in a gas in different direction at randomly.
Q.20 Explain why the temperature of gas drops in an adiabatic expansion?
Answer: During an adiabatic process, a gas has to do work at the cost of its internal energy. When the gas expands, it has to do work, against the surroundings. Since no energy is available externally for this work, hence its internal energy and the temperature fall.
Q.21 Can a given amount of mechanical energy be completely converted into heat?
Answer: Yes, mechanical energy can be converted into heat energy by rubbing hands
Q.22 What causes water pipes to burst in the winter?
Answer: In winter the temperature of the water decreases and become ice in the pipes. The volume of ice increases in the pipes so the pipes bursts in the winter.
Q.23 Why must heat energy be supplied to melt ice after all, the temperature does not changes?
Answer: The amount of heat supplied to the ice is used in latent heat of fusion of ice for this reason the temperature does not change.
Q.24 Can heat be added to substance without changing its temperature?
Answer: Yes, during Isothermal expansion when heat added and the volume of the gas which is enclosed in the cylinder is increased then the temperature remains same.
Q.25 What is temperature? How many temperature scale used?
Answer: Temperature: The average kinetic energy of all molecules is called temperature. It is denoted by . Hotness or coldness of the body is called temperature, there are three temperature sales are used to measure the temperature.
- Celsius degree scale
- Fahrenheit degree scale
- Kelvin scale
Q.26 What is the difference between heat and temperature?
Answer:
Heat;
- Total energy of all molecules is called heat.
- Heat is a form of energy which transfers from hot body to cold body .
- Its SI unit is Joule.
- To measure heat we use calorimeter.
Temperature;
- Average energy of all molecules is called temperature.
- Hotness or coldness of the body is called temperature.
- Its SI unit is Kelvin.
- To measure temperature we use thermometer.
Q.27 On a humid day, some say that air is “heavy”. How does the density of humid air compare with that of dry air at the same temperature and pressure?
Answer: Air becomes humid when its oxygen contents decreases and the percentage of low density gas such as nitrogen in it increases. Thus it is wrong to say that humid air is “heavy”. Humidity makes the air less dense rather than the dry air under the conditions of same temperature and pressure
Q.28 Does the concept of temperature apply to vacuum? Consider interplanetary space, for example?
Answer: In an absolutely perfect vacuum, there is no defined temperature at all. The temperature of vacuum is considered to be temperature of its surroundings.
Q.29 Is it possible for a gas to consist of molecules that all have the same speed?
Answer: Since temperature of as gas is directly proportional to the average translational kinetic energy of its molecules, so at any temperature, it is not possible that all of its molecules have the same speed
Q.30 If hot air rises, why is it cooler at the top of a mountain than near the sea level?
Answer: Hot air, on becoming less dense. rise up and suffers expansion. Due to this both its pressure as well as its temperature falls. That is why high altitudes are always colder than the sea level.
Q.31 Is it possible to say that are under the curve in PV diagram gives magnitude of work done on a gas?
Answer: The magnitude of work done on a gas is W=PV. The area under the curve on PV diagram is PV which is also work. Hence, it’s possible to say that area under the curve on PV diagram gives magnitude of work done on a gas.
Q.32 Explain why temperature decrease with height in lower atmosphere?
Answer: The boiling point of a substance is that temperature at which it changes from liquid to gas or vapor. At boiling point, vapor pressure is equal to the pressure above the liquid. As temperature rises, the molecules of liquid start moving more quickly until they escape from the liquid into gas. Hence more temperature is needed to move molecules faster when pressure is increased. The boiling of a liquid depends upon air pressure. The air pressure decreases with altitude so boiling point drops. Hence temperature decreases.
Q.33 Real gases always cool when making a free expansion whereas an ideal gas does not. Explain.
Answer: The molecules of ideal gas are point particles. There is no space between them. The molecules of real gas have free space due to definite diameter. The real gas has ability of compression. That is why real gases always cool when making a free expansion whereas an ideal gas does not.
Q.34 Why does smoke rise, rather than fall, from a lighted candle?
Answer: The smoke rise, rather than fall, from a lighted candle because density of smoke is smaller than density of air.
Q.35 If hot air rises, why it is cooler at the top of mountain?
Answer: Low temperature of gasses can be explained by Joule Thomson effect. According to this effect when a compressed gas is allowed to go a region of low pressure it gets cooled.
At the top of mountains pressure is low so when gas goes from high pressure zone into low pressure zone its temperature decreases. That is why air gets cool.
Q.36 Why does the boiling temperature of a liquid increases with pressure?
Answer: The temperature at which vapor pressure of a liquid becomes equal to the external pressure is called boiling point of liquid. When external pressure is changed its boiling temperature also changes. When external pressure is high, the liquid requires greater amount of heat to equalize with vapor pressure to external Pressure. In this way boiling temperature will increase.
Q.37 Would a gas whose molecules were true geometric points obey the ideal gas laws?
Answer: The gas whose molecules were true geometric points obeys the ideal gas laws because molecules of ideal gases are also point particles.
Q.38 Although real gases can be liquefied, an ideal gas can not be. Explain.
Answer: The molecules of real gas have intermolecular forces and definite diameter. There is space between molecules. Therefore molecules of real gas has ability of compressibility so can be liquefied. The molecules of ideal gas are point particle and having no space among molecules so can not be liquefied.
Q.39 Show that as the volume per mole of a gas increases, the Van de Waal equation tends to the equation of state of an ideal gas.
Answer: The Van der Waal equation of state is written as
![\[\left[P+a\left(\frac{n}{V}\right)^2\right]\left(V-nb\right)=nRT\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-6cd3fb1536f79eef451420190307180c_l3.png "Rendered by QuickLaTeX.com")
![\[\left[P+a\left(\frac{n}{V}\right)^2\right]V\left(1-\frac{nb}{V}\right)=nRT\]](https://quantapublisher.com/wp-content/ql-cache/quicklatex.com-c90a11a439c90e267ec0bbe2dbbe8254_l3.png "Rendered by QuickLaTeX.com")
When volume V increases the term n/V goes to zero. Hence we get PV=nRT.
Q.40 Can ice be heated to a temperature above 0°C without its melting. Can water be cooled to a temperature below 0°C without its freezing?
Answer: The ice can not be heated to a temperature above 0°C without its melting because all the heat supplied is used to change phase. The water can not be cooled to a temperature below 0°C without its freezing because all the heat removed is used to change the phase.
Q.41 Is heat the same as internal energy, if not give an example in which a system internal energy changes without a flow of heat across the system boundary?
Answer: The heat and internal energy are not same. For example, internal energy changes without flow of heat across the system boundary during adiabatic expansion and compression.
Q.42 Give a qualitative explanation of how frictional forces between moving surfaces produce internal energy. Why does reverse process not occur?
Answer: The temperature increases due to frictional forces between moving surfaces. The internal energy is a function of temperature, hence internal energy increases. The reverse process does not occur because temperature can not be converted into friction.
Q.43 List the examples of Brownian motion in physical phenomena.
Answer: The examples of Brownian motion in physical phenomena are
- The motion of insects and birds.
- The motion of dust or smoke particles in the air.
- The motion of gas or liquid molecules along zig-zag path.
