HW09 solutions Recent site activity Physics 193

Homework 9 solutions

Notes: Please keep in mind that most of the problems in MasteringPhysics with numerical answers are randomized for each student. The solutions below correspond to the version of the problem that is in the paper copy of the textbook. There may be some differences between the textbook version and the online version.

1. Reading questions

a. This is true. You get out of the shower and dry yourself off with a towel. You hang the towel to dry. An hour later you come back and the towel is no longer wet, just damp. An hour after that the towel is almost totally dry but not quite. After one more hour the towel is completely dry. This can be explained by suggesting that the water absorbed by the towel is made of tiny entities called molecules that gradually escape into the air.

b. This is not true. Fill a metal sphere with air and seal it. Submerge the sphere in water and heat the water. The temperature of the gas increases as does its pressure, but the volume of the gas

remains the same. It does not decrease. (Only when you increase the pressure of gas keeping its temperature constant is the gas’s volume guaranteed to decrease.)

2. Tutorial (the problem parts plus the hints in MasteringPhysics walk you through how to do it)

3.

The estimated number of hydrogen atoms in the Sun is

N

H= 0.70m

SUN

M

H/NA

= 0.70 2×10 30

kg

(

)

1.0×1023kg

(

)

(

)

=8.4_×1056

4.

We take the density of air to be ρ=₁._{3 kg/m}3. _{Thus, the mass of air exhaled is}

m

ex =ρV = 1.3 kg/m

3

(

)

(

)

kg

The air that you exhale has higher concentration of CO2 and water vapor and less O2. The temperatures between

the air inhaled and air exhaled can also be different.

5.

Let the temperatures be 298 K during the day, and 288 K at night, and volume of the house be 900 m3. Using ideal gas model for air, the number of moles of air that must leave the house in order to maintain a constant pressure is

Δn₌n

2−n1=

P

2V2

RT

2 − P1V1

RT

1

=

1_.0×105

N/m2

(

)

(

)

8_.3 J/mol⋅K

(

)

1

288 K− 1

298 K

⎛ ⎝⎜

⎞

⎠⎟ =1.26×10 3

mol

6.

n₌ PV RT =

1_.0_×105 N/m2

(

)

(

)

8_.3 J/mol_⋅K

(

)

(

)

0_.021 mol

Since only about 21% of air is O2, the number of oxygen molecules you breathe in each time is

N

O

2