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In the low-temperature limit (kT « E), each term in the rotational partition function (equation 6.30) is much smaller than the one before. Since the first term is independent of T, cut off the sum after the second term and compute the average energy and the heat capacity in this approximation. Keep only the largest T-dependent term at each stage of the calculation. Is your result consistent with the third law of thermodynamics? Sketch the behavior of the heat capacity at all temperatures, interpolating between the high-temperature and low-temperature expressions.
Zrot = j=0∑∞ (2j+1)e-E(j)/kT = j=0∑∞ (2j+1)e-j(j+1)e/kT
A special electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop at an amusement park. The sensor gauges the magnitude of the normal force that the seat exerts on a rider. The loop-the-loop ride is in the..
A 640- hollow ball 25cm in diameter is suspended by a wire and is undergoing torsional oscillations at a frequency of 0.78 Hz .What is the torsional constant of the wire?
two 2cm x 2cm plates that form a parallel capacitor are charged to 0.708 nc. what are the electric field strength
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You throw a ball horizontally off a roof. the time until it lands is determined only by The height of the roof and it's initial speed
In the lungs there are tiny sacs of air, which are called alveoli. Assume the average diameter of one of these sacs is 0.27 mm. An oxygen molecule (mass = 5.3 10-26kg) trapped within a sac and the uncertainty in its position is 0.12 mm. W
The planet Mercury has a mass that is 5.00% of that of Earth, and its gravitational acceleration is gmercury = 3.70 m/s2. a) How long does it take for a rock that is dropped from a height of 2.63 m to hit the ground on Mercury?
A 1000 kg roller coaster car starts from rest from a hilltop 80.0 m above the ground, find the average frictional force between the car's wheels and the track
A 65kg Bicyclist rides 88kg bicycle with a speed of 40m/s. (a) How much work must be done by the brakes to bring the bike and rider to a stop? (b) how far does the bicycle travel if it takes 4.0 second to come to rest? (c) What is the magnitude of..
An automobile of mass 1500 kilogram moving at 25.0 m/s collides with a truck of mass 4500 kilogram at rest. Determine the final velocity of that car and truck just after the collision
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