Answer:
ΔU = - 310.6 J (negative sign indicates decrease in internal energy)
W = 810.6 J
Explanation:
a.
Using first law of thermodynamics:
Q = ΔU + W
where,
Q = Heat Absorbed = 500 J
ΔU = Change in Internal Energy of Gas = ?
W = Work Done = PΔV =
P = Pressure = 2 atm = 202650 Pa
ΔV = Change in Volume = 10 L - 6 L = 4 L = 0.004 m³
Therefore,
Q = ΔU + PΔV
500 J = ΔU + (202650 Pa)(0.004 m³)
ΔU = 500 J - 810.6 J
<u>ΔU = - 310.6 J (negative sign indicates decrease in internal energy)</u>
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b.
The work done can be simply calculated as:
W = PΔV
W = (202650 Pa)(0.004 m³)
<u>W = 810.6 J</u>
(2.00 hours) x (3,600 seconds/hour) = 7,200 seconds
(9.00 minutes) x (60 seconds/minute) = 540 seconds
The record time = (7,200 + 540 + 21) = 7,761 seconds
Distance = (speed) x (time)
= (5.436 m/s) x (7,761 sec) =<span> 42,188.8 meters
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The official length of the marathon run is 42,195 meters.
If we divide that by the record time in the question, we get
5.4368... m/s .
Rounded to the nearest thousandth, that's 5.437 m/s.
If the question had given the speed as 5.437 instead of 5.436 ,
then we would have calculated the distance to be
(5.437 m/s) x (7,761 sec) =<span> 42,196.6 meters,
4.6 meters closer to the official distance than the answer we did get.
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