10. 100 gm of water at 0 °C is mixed with an equal mass of water at 80 °C. Calculate the resultant increase in entropy.

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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1. How far from the earth must a body be along a line toward the sun so that the sun's
gravitational pull balances the earth's? The sun is 9.3 x 10" miles away and its mass is
3.24 x 10° M.
2. (a) With what horizontal speed must a satellite be projected at 100 miles above the
surface of the earth so that it will have a circular orbit about the earth? Take the earth's
radius as 4000 miles. (b) What will be the period of rotation?
3. A block is on a horizontal surface which is moving horizontally with a simple
harmonic motion of frequency two oscillations per second. The coefficient of static
friction between block and plane is 0.50. How great the amplitude be if the block does
not slip along the surface?
4. Show that the maximum tension in the string of a simple pendulum, when the
amplitude 0, is small, is mg(1+0²). At what position of the pendulum is the tension a
maximum?
5. (a) Prove that in simple harmonic motion the average potential energy equals the
average kinetic energy when the average is taken with respect to time over one period
of the motion, and that each average equals kA?/4. (b) Prove that when the average is
taken with respect to position over one cycle, the average potential energy equals kA?/6
and the average kinetic energy equals kA?/3. (c) Explain physically why the two results
above (a and b) are different.
6. A wave if frequency 500 cycles /sec has a phase velocity of 350 meters/sec. (a) How
far apart are two points 60° out of phase? (b) What is the phase difference between two
displacements at a certain point at times 103 sec apart?
7. What is the speed of a transverse wave in a rope of length 2 meters and mass 0.06
kg under a tension of 500 nt?
8. The equation of a transverse wave travelling in a rope is given by
y = 60 cos (0.005x – 8.0t – 0.57),
in which x and y are expressed in centimeters and t in seconds. Write down the equation
of a wave that when added to the given one, would produce standing waves on the rope.
9. A Carnot's engine whose temperature of the source is 400 K takes 500 calories of
heat at this temperature and rejects 400 calories of heat to the sink. What is the
temperature of the sink? Calculate the efficiency of the engine.
10. 100 gm of water at 0 °C is mixed with an equal mass of water at 80 °C. Calculate
the resultant increase in entropy.
Transcribed Image Text:1. How far from the earth must a body be along a line toward the sun so that the sun's gravitational pull balances the earth's? The sun is 9.3 x 10" miles away and its mass is 3.24 x 10° M. 2. (a) With what horizontal speed must a satellite be projected at 100 miles above the surface of the earth so that it will have a circular orbit about the earth? Take the earth's radius as 4000 miles. (b) What will be the period of rotation? 3. A block is on a horizontal surface which is moving horizontally with a simple harmonic motion of frequency two oscillations per second. The coefficient of static friction between block and plane is 0.50. How great the amplitude be if the block does not slip along the surface? 4. Show that the maximum tension in the string of a simple pendulum, when the amplitude 0, is small, is mg(1+0²). At what position of the pendulum is the tension a maximum? 5. (a) Prove that in simple harmonic motion the average potential energy equals the average kinetic energy when the average is taken with respect to time over one period of the motion, and that each average equals kA?/4. (b) Prove that when the average is taken with respect to position over one cycle, the average potential energy equals kA?/6 and the average kinetic energy equals kA?/3. (c) Explain physically why the two results above (a and b) are different. 6. A wave if frequency 500 cycles /sec has a phase velocity of 350 meters/sec. (a) How far apart are two points 60° out of phase? (b) What is the phase difference between two displacements at a certain point at times 103 sec apart? 7. What is the speed of a transverse wave in a rope of length 2 meters and mass 0.06 kg under a tension of 500 nt? 8. The equation of a transverse wave travelling in a rope is given by y = 60 cos (0.005x – 8.0t – 0.57), in which x and y are expressed in centimeters and t in seconds. Write down the equation of a wave that when added to the given one, would produce standing waves on the rope. 9. A Carnot's engine whose temperature of the source is 400 K takes 500 calories of heat at this temperature and rejects 400 calories of heat to the sink. What is the temperature of the sink? Calculate the efficiency of the engine. 10. 100 gm of water at 0 °C is mixed with an equal mass of water at 80 °C. Calculate the resultant increase in entropy.
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