PHY 1151

Hour Exam 4

December 11, 2002

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1. (13.5) A goose-down sleeping bag has a surface area of 2.25 m2 and is filled with a layer of down 5 cm thick. What is the heat-transfer rate (Hcd) through it from a person with skin temperature of 35°C to the outside air at -5°C. How does this rate compare with the body’s minimal metabolism rate, about 100 W?
From Table 13,1, p 457, we find the thermal conductivity of goose down to be
K = 0.023 W/m C°

We can now apply the conduction heat-transfer equation, Eq 13.1,

Hcd = [K A (T2 - T1)] / L

From the problem, we know the other pieces of this equation,

T = T2 - T1 = 35°C - (- 5°C) = 40 C°
A = 2.25 m2
L = 5 cm = 0.05 m
Hcd = [K A (T2 - T1)] / L
Hcd = [(0.023 W/m C°)(2.25 m 2)(40 C°)]/0.05 m =
Hcd = 41 W

This is about half of the body’s normal metabolism so this sleeping bag should keep our camper a “happy camper” (or, at least, a warm camper).

2. (14.1) An ideal gas is sealed in a rigid container at 25°C and 1.0 atm. What will its temperature be when the pressure is incresed to 2.0 atm?

What will its pressure be when the temperature is increased to 50°C

The ideal gas law is
PV = nRT

Being in a rigid container, the gas’ volume does not change; V = Vo = constant. That means we can use the ideal gas law as

T/P = To/Po

or

T = P [ To/Po ] = [ P/Po ] To

Remember, these temperatures must be absolute temperatures,

To = 25°C = 298 K
T = [ P/Po ] To = [2.0 atm/1.0 atm] [298 K] = [ 2 ] [ 298 K] = 596 K
T = 596 K = (596 - 273)°C = 323°C = T

Or, while V = const, we can write the ideal gas law as

P/T = Po/To

or

P = T [ Po/To ] = [ T/To] Po

Remember, these temperatures must be absolute temperatures, measured in Kelvins, K.

To = 25°C = 298 K and T = 50°C = 323 K
P = [ T/To ] Po
P = [ 323 K/296 K ] (1 atm)
P = 1.08 atm

3. (15.31 A 50-g (0.050 kg) mass hanging from a spring oscillates with a frequency of 2 Hz. What is the spring constant?

f 2 = (1/2 ) 2 (k/m)
f 2 = (1/4 2)(k/m)
k = 4 2 f 2 m
k = 4 2 [2 (1/s)] 2 (0.050 kg)
k = 7.9 kg/s2
k = 7.9 N/m

4. (16.49) A train whistle sounds at 500 Hz under normal, stationary conditions.
a) What frequency is heard by a stationary observer when the train approaches at 25 m/s?
b) What frequency is heard by a stationary observer when the train moves away at 25 m/s?


f ' = (500 Hz) (1.079) = 540 Hz



f ' = (500 Hz) (0.932) = 466 Hz

5. Concept Questions:
i) We have considered heat transfer by conduction, convection, and radiation. What is the difference between conduction and convection?

There is no movement of mass (like air or water) with conduction but there is with convection

ii) What is the First Law of Thermodynamics?

The First Law of Thermodynamics is basically Energy Conservation or the Work - Energy Theorem. The change in the internal energy of a system is equal to the heat that flows into the system minus the work done by the system

E = Q – W

iii) Suppose we find the period of a horizontal mass-and-spring simple harmonic oscillator. If we now suspend the same mass on the same spring so it oscillates vertically, how will the period be effected?

The period remains unchanged.


iv) What are longitudinal and transverse waves? How are they different? What do they have in common?

The movements of individual pieces of a longitudinal wave are in the same direction as the wave itself. The movements of individual pieces of a transverse wave are perpendicular to the direction of the wave itself.
Both longitudinal and transverse waves have amplitudes, frequencies, periods, and wavelengths.

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