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1. As a result of some process, the internal energy of a system is increased. According to the first law of thermodynamics, ∆Eint=Q+W. How can one tell that the increase was due to orderly macroscopic workWor due to the flow of energy through disorderly microscopic meansQ? (a) By measuring the temperature of the system before and after the process. (b) By measuring the temperature of the surroundings before and after the process. (c) It is not possible to distinguish betweenWandQ. (d) Both (a) and (b) are correct.Answer 1:
(a) is incorrect because the internal energy has disordered (random) and ordered parts. You can change the internal energy without change in temperature. For example, by bringing a magnet close to or moving it away from an iron piece, the iron can be magnetized or demagnetized. Its internal energy therefore changes (e.g. it can subsequently do work by lifting an iron piece). Yet its temperature hasn't changed. OnceWorQhas been transferred to a system, it is difficult to tell what caused a change in the internal energy to begin with. This is like depositing money in a "bank". Once the money is there, it is unnecessary to know, where the money came from. The only way to tell whetherWorQcontributed to the change in internal energy is by looking at the surroundings. For example, measure its temperature. If the temperature goes down, there has been a flow of energyQfrom the surrounding to the system. Hence the correct answer is (b). 2. Man learnt the use of fire to raise the temperature of objects much earlier than the use of mechanical work, e.g. in steam engines. Could you think of a reason why this could be true?Answer 2:
Fire results in chaotic motion of air molecules in contact with an object whom we wishDate: 12 Sep, 20121
Max. marks:15Time Allowed:15 minutes
to call "heat".This process involves the disorganized, unconstrained collisions between molecules. Mechanical work, however requires a much higher degree of ordered control and hence sophistication. Therefore one could imagine that man mastered the use of fire much earlier than steam engine could be invented. 3. What temperature is required to have 25% of H atoms in the first excited state and75% in the ground state? The value ofkBis 8.6105eV/K
(a) room temperature300 K (b)9.9104K (c)7.4104K (d)2.5104K (e) infinite temperature.Answer 3:
Since we know that, for hydrogen atom,
N 2 N1+N2= 0.25 =1
4 N 1+N2 N 2= 4 N 1 N2+ 1 = 4
N 1 N 2= 3 N 2=N1 3 N2 N 1=1 3 = exp( (E2E1) k BT) (E2E1) kBT= ln1
3 (E2E1) kBT= ln3
)T=E2E1 k Bln310.2 eV
8.6105eV/Kln310104K.
Hence (b) is the correct answer.
4. Blow air onto your hand with your mouth wide open and then your lips puckered. When does the air look cooler and why? Assume the process is so fast thatQ= 0Date: 12 Sep, 20122
Max. marks:15Time Allowed:15 minutes
(i.e. the process is adiabatic.) (a) (b)Answer 4:
It is cooler when the lips are puckered. As air is blown out of the lips, it expands. The expanding breath of air does orderly, macroscopic work on its surroundings pushing molecules away,W <0. As a result the internal energy decreases, ∆Eint=W+Q=W <0. This causes the air to become cooler.
5. Molecules in the combustion chamber of a rocket engine are in a high state of random motion. When the molecules are expelled through a nozzle in a more ordered state, what will their temperature be as their temperature in the chamber before being ex- hausted? AssumeQ= 0. (a) temperature will be lower (b) temperature will be higher (c) temperature will be the same (d) we can't be sure.Answer 5:
In adiabatic expansion work is done on the cost of internal energy, lowering the tem- perature of the molecules in the chamber, therefore (a) is correct. Same reasoning applies asQ4. 6. Meteorologists use the first law of thermodynamics in its adiabatic form (i.e.Q= 0). Using statement of the first law, argue why the temperature in a rising cloud falls as it goes to higher altitudes?Date: 12 Sep, 20123
Max. marks:15Time Allowed:15 minutes20 Co
10 C5 C
o o increasing altitude (a) the temperature falls because we are away from the warm surface of the earth. (b) the temperature falls because the air pressure decreases with altitude, and the cloud expands. (c) the temperature falls because the internal energy of the cloud decreases due to reduced pull of gravity. (d) the temperature falls because the air pressure decreases with the altitude, and the cloud contracts.Answer 6:
The temperature falls because the air pressure decreases with altitude, and the cloud expands, therefore (b) is right. 7. What happens to the air temperature in a valley when cold air blowing from the mountain tops descends into the valley?cold air blows incold air blows in air can't escape from the valley (a) the valley's temperature drops. (b) the valley's temperature rises. (c) there is no change in temperature. (d) more than one of these possibilities are correct.Answer 7:
As air descends into the valley, it compresses air already present. The increase in pressure on the valley's air means work is done on the system,W >0. Hence ∆Eint= W+Q=W >0. The temperature goes up. Therefore (b) is correct answer.Date: 12 Sep, 20124
Max. marks:15Time Allowed:15 minutes
8. A bottle contains a gas of atoms. Each atom has three energy levels as shown.EE E 12 3400 nm200 nmIncident radiation
Emitted radiation
Ultraviolet photons of wavelength 200 nm shine on the atom, enabling the transition fromE1toE3. However only a violet photon of wavelength 400 nm is emitted as a result of a downward transition. Where does the "missing energy" go? (a) The incident photon is scattered carrying away the missing energy. (b) The energy of the 400 nm photon adjusts itself to make up for the missing energy. (c) Energy need not be conserved. (d) The atom will undergo centre of mass motion with energyE3E2. (e) The gaseous atoms collide with one another, transferring the residual energyE3E2 to one another.Answer 8:
Since the incident photon is wholly absorbed, the process cannot result in centre of mass motion, as would happen in (a) or (d). Energy must be conserved. The only possibility that remains is (e). Collision between the gaseous atoms results in the atom losing its excess energy, contributing to the disordered motion of the gas molecules, hence increasing the temperature. 9. The rotational energy levels in a molecule are quantized byErot,ℓ=L22I=ℓ(ℓ+1)~2
2I, where the symbols have the usual meanings andℓ= 0,1,2,....is the rotational quan- tum number. In which of these molecules, there will be the highest population in the first excited stateErot,1at a temperature of 10 K? (a)H2(b)O2(c)N2(d)I2. The moments of inertia for these molecules (in the units of 1038gcm2) areH2= 0.05,
O2= 0.2,N2= 0.14,I2= 7.5.
Answer 9:
Date: 12 Sep, 20125
Max. marks:15Time Allowed:15 minutes
The energy spacing between theℓ= 0 andℓ= 1 levels is2~2 2I=~2 I . The spac- ing is smallest for largestI. HenceErot,1will have the most population for theI2 molecule. Lower energies mean higher populations because of the Boltzmann factor /exp(E k BT). 10. The diagram shows the potential energy curve for two atoms brought close to one another. The energy of the system is shown by the dashed line. At which of the points A, B, C, will the force be maximum and in what direction?A BC r Ou(r) (a) At A, repulsive. (b) At A, attractive. (c) At B, attractive. (d) At C, attractive. (e) At C, repulsive.Answer 10:
The force is given by the negative of the slope,du(r)/dr. The magnitude of the slope is largest at C and the direction of the slope is negative, which means that the force is positive, indicating repulsion.Date: 12 Sep, 20126
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