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1) A steel guitar string is streched between supports 85.2 cm apart. When the temperature is 0 °C, the fundamental frequency of transverse oscillations of the string is 201.5 Hz. What will be the value of fundamental frequency in Hz if the temperature is raised to 53.6 °C? (Error of answer is tolerated within ±0.1 Hz, Do not include units in the answer box)
Useful Data:
mass density of steel is: 7,860 kg/m3
Young’s modulus of steel is 200,000,000,000 N/m2 (20×1010 N/m2)
Coefficient of thermal expansion of steel is: 0.000011 (C°)-1
2) Assume you have a diatomic gas initially at pressure p0 and initial volume V0. If you compress the gas isothermally to a 71.6% of its initial volume, the final pressure is p1. If you compress it adiabatically to same final volume, the final pressure is p2. What is the ratio p1/p2?
3) You can excite waves in a string of length 1.821 m fixed at both ends. You started from an arbitrarily low frequency and increased it slowly. You found two successive harmonic standing waves of frequencies: 214.7 Hz and 225.5 Hz. What is the speed of the wave in the medium in m/s.
Note that the speed of standing waves is zero, because it is composed of two waves of velocities
v and –
v. The question is about the magnitude of
v and the answer is not zero!
PHYSICS
2
2
1
Summer 201
3
Homework 8 Wednesday
August 7, 2013
1. Two moles of an ideal diatomic gas have an initial pressure of
4
.00 atm and initial volume
of 16.0 L. The molecules in the gas can translate and rotate but not vibrate. The gas is
compressed at constant pressure to a new volume of 8.00 L.
(a) What are the initial and final temperatures of the gas?
(b) How much work is done by the gas during this process?
(c) How much heat is absorbed by the gas during this process?
(d) What is the change in the internal energy of the gas during this process?
2. An ideal gas mixture consists of n1 moles of a pure gas whose molar heat capacity at constant
volume is R/ (γ1 − 1) and n2 moles of a pure gas whose molar heat capacity at constant
volume is R/ (γ2 − 1). Find:
(a) the total heat capacity (at constant volume) of the sample, and
(b) the total heat capacity at constant pressure.
1
PHYSICS 221
Summer 2013
Homework 8 Wednesday
August 7, 2013
3. 4 moles of an ideal gas have an initial temperature of 127 ◦C. The temperature of the gas
is kept constant and the volume is increases until the pressure drops to 40.0% of its original
value.
(a) Draw a p−V diagram for this process
(b) Calculate the work done by the gas.
(c) What is the change in internal energy of the gas?
(d) Calculate the heat added to the gas.
4. A gas with a volume of 4.0 L is at a pressure of 1.0 atm at a temperature of 300 K. It is
compressed adiabatically to a volume of 1.0 L. The gas has γ = 1.4.
(a) Determine the final pressure.
(b) Determine the final temperature.
2
PHYSICS 221
Summer 2013
Homework 8 Wednesday
August 7, 2013
5. Four moles of an ideal monatomic gas, with a ratio of heat capacities γ = 1.67, initially have a
pressure p1 = 2.00 atm, a volume V1 = 45.0 L and a temperature T1. Then the gas undergoes
the following three-step cyclic process, as shown in the p−V diagram below.
(i) Adiabatic expansion from the temperature T1, pressure p1, and volume V1 to a temperature
T2, volume V2 = 65.0 L and pressure p2.
V (L)
p(Tm)
45 50 55 60 65 70
2 1
2
3
i
ii
iii
(ii) Increase in pressure at constant vol-
ume to a pressure p3 and a temper-
ature T3.
(iii) Isothermal compression to the orig-
inal starting pressure, volume, and
temperature.
(a) What is T1?
(b) What are T2 and p2?
(c) What are T3 and p3?
(d) From the figure, is the net work done by the gas during the cycle positive or negative?
(e) What is the work done by the gas during each of the three steps of the cycle? What is
the net work done by the gas during the entire cycle?
(f) How much heat is absorbed by the gas during each of the three steps of the cycle? What
is the net heat absorbed by the gas during the entire cycle? Why should this last result
be exactly the same as the last result in part (e)?
3
PHYSICS 221
Summer 2013
Homework 8 Wednesday
August 7, 2013
6. A diatomic ideal gas is taken through the cycle shown in the figure in the direction a → b →
c → a. What is the efficiency of this cycle?
V (m3)
p(×105 Pa)
0.500 0.800
1.00
3.00 a b
c
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