(a)
The number of microstates available to the combined system.
(a)
Answer to Problem 81PQ
The number of microstates available to the combined system is
Explanation of Solution
The number of microstates for the combined system is the product of microstates of individual systems.
Write the expression to calculate the microstates of the combined system.
Here, w is the microstates of the combined system,
Conclusion:
Substitute
Therefore, the number of microstates available to the combined system is
(b)
The entropies of the systems A,
(b)
Answer to Problem 81PQ
The entropies of the systems A,
Explanation of Solution
Write the expression to calculate the entropy of the system
Here,
Write the expression to calculate the entropy of the system
Here,
Write the expression to calculate the entropy of the system
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the entropies of the systems A,
Want to see more full solutions like this?
Chapter 22 Solutions
Physics for Scientists and Engineers: Foundations and Connections
- In the text, it was shown that N/V=2.681025m3 for gas at STP. (a) Show that this quantity is equivalent to N/V=2.681019cm3, as stated. (b) About how many atoms are mere in one m3 (a cubic micrometer) at STP? (c) What does your answer to part (b) imply about the separation of Mama and molecules?arrow_forwardIn the deep space between galaxies, the number density of atoms is as low as 106 atoms/m3, and the temperature is a frigid 2.7 K. a)What is the pressure, in pascals, in the region between galaxies? b)What volume, in cubic meters, is occupied by 1.5 mol of gas? c)If this volume is a cube, what is the length of one of its edges, in kilometers?arrow_forwardIn the deep space between galaxies, the density of molecules (which are mostly single atoms) can be as low as 106 atoms/m3, and the temperature is a frigid 2.7 K. What is the pressure? (b) What volume (in m3 ) is occupied by 1 mol of gas? (c) If this volume is a cube, what is the length of its sides in kilometers?arrow_forward
- A)An ideal gas is confined to a container at a temperature of 330 K.What is the average kinetic energy of an atom of the gas? (Express your answer to two significant figures.) B)2.00 mol of the helium is confined to a 2.00-L container at a pressure of 11.0 atm. The atomic mass of helium is 4.00 u, and the conversion between u and kg is 1 u = 1.661 ××10−27 kg.Calculate vrmsvrms. (Express your answer to three significant figures.) C)A gold (coefficient of linear expansion α=14×10−6K−1α=14×10−6K−1 ) pin is exactly 4.00 cm long when its temperature is 180∘∘C. Find the decrease in long of the pin when it cools to 28.0∘∘C? (Express your answer to two significant figures.)arrow_forwardIn the deep space between galaxies, the density of atoms is 1 million atoms per m3 (i.e. there are 1 million atoms in a cubic meter), and the temperature is 3 K. (a) What is the pressure in space? (b) What volume (in cubic meters) is occupied by 100 moles of space gas? (c) If this volume is a cube, what is the length of one its sides in kilometers?arrow_forward(a) What is the coefficient of variation (CV)? Why do you study such variations? Explain using a real-life example.(b) Among the different measures of dispersion which one do you think is better and why?The following table gives the distribution of gas bills (GB’s) of some households (hhs) in a city- GB’s ($.’0) No. of hhs 375-450 41 450-525 95 525-600 31 600-675 61 675-750 19 (i) Calculate the ideal measures of dispersion.(ii) Make comments from your findings.arrow_forward
- (a) How many molecules are present in a sample of an ideal gas that occupies a volume of 2.30 cm3, is at a temperature of 20°C, and is at atmospheric pressure? molecules (b) How many molecules of the gas are present if the volume and temperature are the same as in part (a), but the pressure is now 1.30 ✕ 10−11 Pa (an extremely good vacuum)?arrow_forward(a) How many molecules are present in a sample of an ideal gas that occupies a volume of 2.70 cm3, is at a temperature of 20°C, and is at atmospheric pressure? ?molecules (b) How many molecules of the gas are present if the volume and temperature are the same as in part (a), but the pressure is now 1.60 ✕ 10−11 Pa (an extremely good vacuum)? ?moleculesarrow_forward(a) What is the total translational kinetic energy of the air in an empty room that has dimensions 8.00 m * 12.00 m * 4.00 m if the air is treated as an ideal gas at 1.00 atm? (b) What is the speed of a 2000 kg automobile if its kinetic energy equals the translational kinetic energy calculated in part (a)?arrow_forward
- A 689.00g block of gold ( cgold=129 J kg°C ) initially at 15.00°C is placed in thermal contact with an unknown mass of aluminum ( calum=900 J kg°C ) initially at 90.00°C . If they equilibrate at a final temperature of 68.00°C , what is the mass of the aluminum? g What assumption do we make when solving calorimetry problems like this? We can only have two substances in thermal contact. The substances are in a closed, isolated container that does not allow any energy to enter or leave the system. The two substances must have different specific heats. Some of the energy transferred from one substance is lost to its surroundings and does not go to the other substance.arrow_forward(a)In the deep space between galaxies, the density of atoms is as low as 106 atoms/m3, and the temperature is a frigid 2.7 K. What is the pressure (in Pa)? ____________________ Pa (b)What volume (in m3) is occupied by 6 mol of gas? ______________________ m3 (c)If this volume is a cube, what is the length of its sides in kilometers? ________________ kmarrow_forwardThe mass of a single hydrogen molecule is approximately 3.32 1027 kg. There are 5.64 1023 hydrogen molecules in a box with square walls of area 49.0 cm2. If the rms speed of the molecules is 2.72 103 m/s, calculate the pressure exerted by the gas.arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College