## Fluids, Gases, Thermodynamics

• Fluids
Pressure, Buoyancy, Bernoulli’s Principle, equation of continuity
• Thermal properties of matter
Temperature, Thermal Expansion, Thermal Conductivity, Specific and Latent Heat, Heat Transfer, Radiation laws
• Gases
Ideal Gas Law, Kinetic Theory, Maxwell distribution, Boltzmann distribution
• The Laws of Thermodynamics
Thermodynamic processes, 1st and 2nd law of thermodynamics, Carnot Engines, Heat Engines, Heat Pumps and Refrigerators, Entropy

### Problem 1:

Water flows through a Venturi tube as shown in the diagram. The radius of the large cross section of the pipe is 2 cm and the radius of the constricted portion of the pipe is 1 cm.  If the speed of the water in the large cross section pipe is 1 m/s, the pressure difference (P1 - P2) is most nearly

(A)  0.6*102 N/m2    (B)  3*102 N/m2    (C)  1.5*103 N/m2    (D)  7.5*103 N/m2   (E)  37.5*103 N/m2

### Problem 2:

The Maxwell distribution of molecular speeds in a gas is given by
n(v) = A v2 exp(-mv2/(2kT)),
where A is a constant.
The most probable speed is

(A)  (2kT/m)½    (B)  (3kT/m)½    (C)  (8kT/m)½    (D)  3kT/2   (E)  (2π m kT)½

### Problem 3:

A mole of ideal gas initially at temperature T0 and volume V0 undergoes a reversible isothermal expansion to a volume V1.  If the ratio of the specific heats is cP/cV = γ an if R is the gas constant, the work done is

(A)  0    (B)  RT0 (V1/V0)γ    (C)  RT0 (V1/V0 - 1)    (D)  CVT0 [1 - (V0/V1)γ]   (E)  RT0 ln(V1/V0)

### Problem 4:

Electric power is used to heat and melt 3 kg of a certain material.  The graph of temperature versus time for the process is shown.  A current of 10 A at a potential difference of 100 V is used and the time between t1 and t2 is approximately 15 minutes.  The heat of fusion of the material is most nearly

(A)  80 J/kg    (B)  970*102 J/kg    (C)  144*103 J/kg    (D)  340*103 J/kg    (E)  539*1032 J/kg

### Problem 5:

Assuming that all the planets have the same reflection coefficient for sunlight and the same emission coefficient, which of the following relationships would be expected between the planets average temperatures T in Kelvin and their distance R from the sun?

(A)  T ∝ R-2    (B)  T ∝ R-1    (C)  T ∝ R    (D)  T ∝ R½    (E)  T ∝ R2

### Problem 6:

In terms of the Boltzmann constant, the classical constant-volume specific heat per atom of He gas is

(A)  k/2   (B)  k    (C)  (3/2)k    (D)  2k    (E)  3k

### Problem 7:

A gas is take through the cycle A --> B --> C --> A as shown.  What is the net work done by the gas?

(A)  2000 J   (B)  1000 J    (C)  0 J    (D)  -1000 J    (E)  -2000 J

### Problem 8:

A thermodynamic system, initially at absolute temperature T1, contains a mass m of water with specific heat capacity c.  Heat is added until the temperature rises to T2.  The change in entropy of the water is

(A)  0    (B)  T2 - T1   (C)  mcT2   (D)  mc(T2 - T1)    (E)  mc ln(T2/T1)

### Problem 9:

Heat dQ flows from a body of temperature T1 to a body of temperature T2.  The total change in the entropy of the two bodies is equal to

(A)  dQ(1/T1 + 1/T2)    (B)  dQ(T1 + T2)   (C)  dQ(T1 - T2)   (D)  -dQ(1/T1 - 1/T2)    (E)  dQ/T2

### Problem 10:

Refer to the following processes involving systems labeled by numbers 1 - 8.

A bar of iron (1) at 300 K is brought into thermal contact with a body (2) at 400 K, the two being thermally isolate from all other systems.
An ideal gas (3) is compressed reversibly while in contact with a reservoir (4), the two being thermally isolate from all other systems.
A body of water (5) freezes reversibly.
A container of water is stirred and its temperature increases by 1 K.
A chemical reaction takes place in an isolated system (7).
A Carnot engine (8) operates in a cycle.

For which of the systems does the entropy decrease?

(A)  1    (B)  4   (C)  5   (D)  6    (E)  7