Concept explainers
(a)
The rms speed of the molecule for a particular diameter.
(a)
Answer to Problem 61AP
The rms speed of the molecule is
Explanation of Solution
Write the expression for volume of the particle.
Here,
Write the expression for mass in terms of density and volume.
Here,
Write the expression for kinetic energy of the particle.
Here,
Conclusion:
Substitute equation (I) in equation (II).
Here,
Substitute above equation in the equation (III) instead of mass.
Substitute
Here,
Therefore, the rms speed of the molecule is
(b)
The time interval of the particle’s actual motion.
(b)
Answer to Problem 61AP
The time interval of the particle’s actual motion is
Explanation of Solution
Write the expression for the distance of the particle equal to its dimeter.
Here,
Rearrange the above equation for
Conclusion:
Substitute
Here,
Therefore, the number of moles of air in the pump is
(c)
The rms speed and time interval of the particle for diameter
(c)
Answer to Problem 61AP
The rms speed is
Explanation of Solution
Write the expression for rms speed of the particle.
Conclusion:
Substitute
Substitute
Therefore, the rms speed is
(d)
The rms speed and time interval of the particle for a sphere.
(d)
Answer to Problem 61AP
The rms speed is
Explanation of Solution
Write the expression for mass of an object in terms of density and volume.
Rearrange the above expression for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the rms speed is
Want to see more full solutions like this?
Chapter 21 Solutions
Physics for Scientists and Engineers with Modern Physics Technology Update
- Cylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false? (a) The two gases haw different temperatures. (b) The temperature of cylinder B is less than the temperature of cylinder A. (c) The temperature of cylinder B is greater than the temperature of cylinder A. (d) The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.arrow_forwardA cylinder with a piston holds 0.50 m3 of oxygen at an absolute pressure of 4.0 atm. The piston is pulled outward, increasing the volume of the gas until the pressure drops to 1.0 atm. If the temperature stays constant, what new volume does the gas occupy? (a) 1.0 m3 (b) 1.5 m3 (c) 2.0 m3 (d) 0.12 m3 (e) 2.5 m3arrow_forwardA gas is at 200 K. If we wish to double the rms speed of the molecules of the gas, to what value must we raise its temperature? (a) 283 K (b) 400 K (c) 566 K (d) 800 K (e) 1 130 Karrow_forward
- A 40.0-g projectile is launched by the expansion of hot gas in an arrangement shown in Figure P12.4a. The cross sectional area of the launch tube is 1.0 cm2, and the length that the projectile travels down the tube after starting from rest is 52 cm. As the gas expands, the pressure varies as shown in Figure P12.4b. The values for the initial pressure and volume are P1 = 11 105 Pa and Vi = 8.0 cm3 while the final values are Pf = 1.0 105 Pa and Vf = 8.0 cm3. Friction between the projectile and the launch tube is negligible, (a) If the projectile is launched into a vacuum, what is the speed of the projectile as it leaves the launch tube? (b) If instead the projectile is launched into air at a pressure of 1.0 105 Pa. what fraction of the work done by the expanding gas in the tube is spent by the projectile pushing air out of the way as it proceeds down tile tube?arrow_forwardAn ideal gas is contained in a vessel at 300 K. The temperature of the gas is then increased to 900 K. (i) By what factor does the average kinetic energy of the molecules change, (a) a factor of 9, (b) a factor of 3, (c) a factor of 3, (d) a factor of 1, or (e) a factor of 13? Using the same choices as in part (i), by what factor does each of the following change: (ii) the rms molecular speed of the molecules, (iii) the average momentum change that one molecule undergoes in a collision with one particular wall, (iv) the rate of collisions of molecules with walls, and (v) the pressure of the gas?arrow_forwardHow many moles are there in (a) 0.0500 g of N2 gas (M = 28.0 g/mol)? (b) 10.0 g of CO2 gas (M = 44.0 g/mol)? (c) How many molecules are present in each case?arrow_forward
- Fifteen identical particles have various speeds: one has a speed of 2.00 m/s, two have speeds of 3.00 m/s, three have speeds of 5.00 m/s, four have speeds of 7.00 m/s, three have speeds of 9.00 m/s, and two have speeds of 12.0 m/s. Find (a) the average speed, (b) the rms speed, and (c) the most probable speed of these particles.arrow_forwardA cylinder that has a 40.0-cm radius and is 50.0 cm deep is filled with air at 20.0C and 1.00 atm (Fig. P10.74a). A 20.0-kg piston is now lowered into the cylinder, compressing the air trapped inside as it takes equilibrium height hi (Fig. P16.74b). Finally, a 25.0-kg dog stands on the piston, further compressing the air, which remains at 20C (Fig. P16.74c). (a) How far down (h) does the piston move when the dog steps onto it? (b) To what temperature should the gas be warmed to raise the piston and dog back to hi?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningPhysics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning