question on waves.?

Question

1) Suppose you are standing by the side of a road in the Sahara desert where the temperature has reached a hot 55.4 oC (132 oF). A truck, traveling at constant speed, passes by. After 3.53 s have elapsed, you use the ultrasonic ruler discussed in Example 4 to measure the distance to the truck. A sound pulse leaves the ultrsonic ruler and returns 1.29 s later. Assume that the average molecular mass of air is 28.9 u, air is an ideal diatomic gas ( = 7/5), and the truck moves a negligible distance in the time it takes for the sound pulse to reach it. Determine how fast the truck is moving.
2)An irreversible engine operates between temperatures of TH = 877 K and TC = 307 K. It absorbs 1270 J of heat from the hot reservoir and does 213 J of work. If the engine were reversible, what is the magnitude |Wreversible| of the work it would have done, assuming it operated between the same temperatures and absorbed the same heat as the irreversible engine?

Answer 1

1) Speed of sound as a function of temperature
Vs(tm)=331.3 sqrt(1+tm/273.15)
Vs(55.4)=331.3 sqrt(1+55.4/273.15)=
Vs(55.4)=363.4 m/sec
Or
Vs= sqrt(gRT/M)
R = the universal gas constant = 8.314 J/mol K,
T = the absolute temperature
M = the molecular weight of the gas in kg/mol (28.9 or .0285 kg/mol)
g = the adiabatic constant, characteristic of the specific gas =7/5
Vs= sqrt(gRT/M)=
Vs=sqrt( (7/5) 8.314 (328.5) /.0289)=
Vs=363.7m/s

State equation for the distance to truck is
S=V1 t1 =Vs t2
t1=3.53 +S/Vs= 3.53 +( 1.29 /2)=4.175 sec [Note 1.29/2 cannot be ignored. If you must set it equal to 0 as required by the statement of the problem)
t2= 1.29 /2=
V1 (4.175 ) =Vs (0.645)
V1= Vs (0.645)/(4.175 )
V1=363.7 x (0.645)/ (4.175 ) =
V1=56.2 m/s

2)
W(reversible) =Q (1-Tc/Th)
Q=1270 J
Tc= 307k
Th=877 K
W(reversible) =1270 (1 - 307/877)
W(reversible) = 825 J