A balloon is equipped with temperature- and altitude-measuring instruments and has
radio equipment that can transmit the output readings of these instruments back to
ground. The balloon is initially anchored to the ground with the instrument output
readings in steady-state. The altitude-measuring instrument is approximately zero
order and the temperature transducer is approximately first order with a time constant
of 10 seconds. The temperature on the ground, T0, is 20C and the temperature Th at
an altitude of x meters is given by the relation: Th ¼ T0 0.012 h
(a) If the balloon is released at time 0, and thereafter rises upward at a velocity of
6 m/s, draw a table showing the temperature and altitude measurements reported
at intervals of 10 seconds over the first 100 seconds of travel. Show also in the
table the error in each temperature reading.
(b) What temperature does the balloon report at an altitude of 8000 m?
(c) What is the error in the temperature reading at this altitude of 8000 m?