- 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

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 (P_{1} - P_{2}) is most nearly

(A) 0.6*10^{2} N/m^{2}
(B) 3*10^{2} N/m^{2} (C)
1.5*10^{3} N/m^{2}
(D) 7.5*10^{3} N/m^{2} (E) 37.5*10^{3}
N/m^{2}

The Maxwell distribution of molecular speeds in a gas is given by

n(v) = A v^{2} exp(-mv^{2}/(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}

A mole of ideal gas initially at temperature T_{0} and volume V_{0}
undergoes a reversible isothermal expansion to a volume V_{1}. If
the ratio of the specific heats is c_{P}/c_{V} = γ an if R is
the gas constant, the work done is

(A) 0
(B) RT_{0 }(V_{1}/V_{0})^{γ} (C)
RT_{0 }(V_{1}/V_{0} - 1)
(D) C_{V}T_{0 }[1 - (V_{0}/V_{1})^{γ}]
(E) RT_{0} ln(V_{1}/V_{0})

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 t_{1}
and t_{2} is approximately 15 minutes. The heat of fusion of the
material is most nearly

(A) 80 J/kg (B) 970*10^{2} J/kg (C)
144*10^{3} J/kg
(D) 340*10^{3} J/kg (E) 539*10^{32}
J/kg

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^{-½}
(D) T ∝ R^{½} (E) T ∝ R^{2}

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

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

A thermodynamic system, initially at absolute temperature T_{1},
contains a mass m of water with specific heat capacity c. Heat is added
until the temperature rises to T_{2}. The change in entropy of the
water is

(A) 0 (B)
T_{2} - T_{1} (C) mcT_{2} (D)
mc(T_{2} - T_{1}) (E) mc ln(T_{2}/T_{1})

Heat dQ flows from a body of temperature T_{1} to a body of
temperature T_{2}. The total change in the entropy of the two
bodies is equal to

(A) dQ(1/T_{1} + 1/T_{2}) (B)
dQ(T_{1} + T_{2}) (C) dQ(T_{1} -
T_{2}) (D) -dQ(1/T_{1} - 1/T_{2})
(E) dQ/T_{2}

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