Question 1

If an ideal gas molecule has a speed of  0.50 km/s at $20 ^ { \circ } \mathrm { C }$ what is its speed at $80 ^ { \circ } \mathrm { C } ?$

Accepted Answer

A)   1000 m/s 
B)   550 m/s 
C)   500 m/s 
D)   2000 m/s

Question 2

Nitrogen boils at $- 196 ^ { \circ } \mathrm { C }$ What is the corresponding temperature in the Fahrenheit scale?

Accepted Answer

A)  $- 321 ^ { \circ } \mathrm { F }$ 
B)  $- 196 ^ { \circ } \mathrm { F }$ 
C)  $- 346 ^ { \circ } \mathrm { F }$ 
D)  $- 315 ^ { \circ } \mathrm { F }$ 
E)  $- 290 ^ { \circ } \mathrm { F }$

Question 3

By what length will a slab of concrete that is originally  18 m  long contract when the temperature drops from $24 ^ { \circ } \mathrm { C } \text { to } - 16 ^ { \circ } \mathrm { C } ?$
The coefficient of linear thermal expansion for this concrete is $1.0 \times$ $10^{ - 5} \mathrm {~K} ^ { - 1 }$

Accepted Answer

A)   1.5 cm 
B)   1.2 cm 
C)   0.50 cm 
D)   0.72 cm

Question 4

At what temperature is the rms speed of hydrogen molecules, $\mathrm { H } _ { 2 }$ which have a molecular weight of  2.02 g/mole, equal to  2.0 km/s? The Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K } \text { and } N _ { \mathrm { A } } = 6.022 \times$ $10^{23}$ molecules/mol.

Accepted Answer

A)  $17 ^ { \circ } \mathrm { C }$ 
B)  $51 ^ { \circ } \mathrm { C }$ 
C)  $72 ^ { \circ } \mathrm { C }$ 
D)  $34 ^ { \circ } \mathrm { C }$ 
E)  $68 ^ { \circ } \mathrm { C }$

Question 5

An ideal gas occupies $6.00 \times 10 ^ { 2 } \mathrm {~cm} ^ { 3 } \text { at } 20 ^ { \circ } \mathrm { C }$ At what temperature will it occupy $1.20 \times 10 ^ { 3 } \mathrm {~cm} ^ { 3 }$ if the pressure is held constant?

Accepted Answer

A)  $100 ^ { \circ } \mathrm { C }$ 
B)  $313 ^ { \circ } \mathrm { C }$ 
C)  $10 ^ { \circ } \mathrm { C }$ 
D)  $40 ^ { \circ } \mathrm { C }$

Question 6

How many molecules are in (a) $1.0 \mathrm {~cm} ^ { 3 }$ of air at STP and (b) $1.0 \mathrm {~cm} ^ { 3 }$ of helium at STP?  (R 
$\left. = 8.31 \mathrm {~J} / \mathrm { mol } . \mathrm { K } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } \right)$

Accepted Answer

The answer of How many molecules are in (a) \(1.0...

Question 7

A 24.0-L tank contains ideal helium gas at $27 ^ { \circ } \mathrm { C }$ and a pressure of  22.0  atm. How many moles of gas are in the tank? $( R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} = 101 \mathrm { kPa } )$

Accepted Answer

A)   138 mol 
B)   17.5 mol 
C)   21.4 mol 
D)   76.0 mol 
E)   238 mol

Question 8

The root-mean-square speed of the molecules of an ideal gas is v. The gas is now slowly compressed to one-half its original volume with no change in temperature. What is the
Root-mean-square speed of the molecules now?

Accepted Answer

A)  $v$ 
B)   $2 v$ 
C)  $v / \sqrt { 2 }$ 
D)  $v / 2$ 
E)  $4 v$

Question 9

The coefficient of linear expansion of aluminum is $24 \times 10 ^ { - 6 } \mathrm {~K} ^ { - 1 }$  \quad  and the coefficient of volume
expansion of olive oil is $0.68 \times 10 ^ { - 3 } \mathrm {~K} ^ { - 1 }$. A novice cook, in preparation of some pesto, fills a 1.00-L
aluminum pot to the brim and heats the oil and the pot from an initial temperature of $15 ^ { \circ } \mathrm { C }$ to
$190 ^ { \circ } \mathrm { C }$ To his consternation some olive oil spills over the top. How much?

Accepted Answer

A)  0.14 L 
B)  0.12 L 
C)  0.13 L 
D)  0.11 L 
E)  0.15 L

Question 10

A vertical cylinder, closed at the bottom end, contains  0.0100  mol of ideal gas. It is fitted at the top with a piston that can move freely. The mass of the piston is  14.0 kg and the initial height of the piston above the bottom of the cylinder is  25 cm. What is the temperature of the gas? $( R = 8.31$ $\mathrm { J } / \mathrm { mol } \cdot \mathrm { K } )$

Accepted Answer

A)   405 K 
B)   3620 K 
C)   413 K 
D)   500 K 
E)   290 K

Question 11

An aluminum rod is  10.0 cm long and a steel rod is  80.0 cm long when both rods are at a temperature of $15 ^ { \circ } \mathrm { C }$ Both rods have the same diameter. The rods are now joined end-to-end to form a rod  90.0 cm  long. If the temperature is now raised from $15 ^ { \circ } \mathrm { C } \text { to } 90 ^ { \circ } \mathrm { C }$ what is the increase in the length of the joined rod? The coefficient of linear expansion of aluminum is $2.4 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$ and that of steel is $1.2 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 }$

Accepted Answer

A)   0.90 mm 
B)   0.81 mm 
C)   0.63 mm 
D)   0.72 mm 
E)   0.99 mm

Question 12

A jar holds  2.0 L of ideal nitrogen gas, $\mathrm { N } _ { 2 }$ at STP. The atomic mass of nitrogen is  14.0 g/mol, the ideal gas constant is $R = 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K }$ Avogadro's number is $N _ { \mathrm { A } } = 6.022 \times$ $10^{23} \text { molecules/mol, }$ and  1.00 atm=101 kPa
(a) How many moles of nitrogen are in the jar?
(b) How many nitrogen molecules are in the jar?
(c) What is the mass of the nitrogen in the jar?

Accepted Answer

The answer of A jar holds  2.0 L of...

Question 13

Platinum melts at $3215 ^ { \circ } \mathrm { F }$ What is the corresponding temperature in the Kelvin scale?

Accepted Answer

A)   2135 K 
B)   3215 K 
C)   2041 K 
D)   2296 K 
E)   2207 K

Question 14

The weather outside is frightful. The temperature is $- 22 ^ { \circ } \mathrm { F }$ What is the corresponding temperature in the Celsius scale?

Accepted Answer

A)  $- 20 ^ { \circ } \mathrm { C }$ 
B)  $- 35 ^ { \circ } \mathrm { C }$ 
C)  $- 30 ^ { \circ } \mathrm { C }$ 
D)  $- 22 ^ { \circ } \mathrm { C }$ 
E)  $- 12 ^ { \circ } \mathrm { C }$

Question 15

An ideal gas is held in a container of volume  V  at pressure  p . The rms speed of a gas molecule under these conditions is $v$ If now the volume and pressure are changed to  2 V  and  2 p , the rms speed of a molecule will be

Accepted Answer

A)  $4 v$ 
B)   
C)  $v / 2$ 
D)  $2 v$ 
E)  $v / 4$

Question 16

The coefficient of linear expansion of copper is $17 \times 10 ^ { - 6 } K ^ { - 1 }$ A block of copper  30 cm wide,  45 cm Iong, and  10 cm thick is heated from $0 ^ { \circ } \mathrm { C } \text { to } 100 ^ { \circ } \mathrm { C }$
What is the change in the volume of the block?

Accepted Answer

A)  $6.9 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$ 
B)  $4.6 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$ 
C)  $14 \times 10 ^ { - 5 } m ^ { 3 }$ 
D)  $2.3 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$ 
E)  $5.2 \times 10 ^ { - 5 } \mathrm {~m} ^ { 3 }$

Question 17

A brass rod is  69.5 cm long and an aluminum rod is  49.3 cm long when both rods are at an initial temperature of $0 ^ { \circ } \mathrm { C }$ The rods are placed in line with a gap of  1.2 cm between them, as shown in the figure. The distance between the far ends of the rods is maintained at  120.0 cm throughout. The temperature of both rods is raised equally until they are barely in contact. At what temperature does contact occur? The coefficients of linear expansion of brass and aluminum are $2.0 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (brass) and } 2.4 \times 10 ^ { - 5 } \mathrm {~K} ^ { - 1 } \text { (aluminum). }$

Accepted Answer

A)  $510 ^ { \circ } \mathrm { C }$ 
B)  $470 ^ { \circ } \mathrm { C }$ 
C)  $440 ^ { \circ } \mathrm { C }$ 
D)  $490 ^ { \circ } \mathrm { C }$ 
E)  $420 ^ { \circ } \mathrm { C }$

Question 18

A gas-filled vertical cylinder, closed at the bottom end, is fitted at the top with a piston that can move freely. The mass of the piston is  10.0 kg, and the initial height of the piston above the bottom of the cylinder is  25 cm. A mass of  8.0 kg is placed on the piston. What is the resulting height of the piston, assuming that the temperature of the ideal gas is kept constant?

Accepted Answer

A)   16 cm 
B)   12 cm 
C)   14 cm 
D)   15 cm 
E)   13 cm

Question 19

A  5.3 L flask of ideal neon gas (which is monatomic) is at a pressure of  6.0  atm and a temperature of  290 K. The atomic mass of neon is  20.2 g/mol. What is the mass of the neon gas in the flask. $( R =$ $\left. 8.31 \mathrm {~J} / \mathrm { mol } \cdot \mathrm { K } , 1 \mathrm {~atm} = 101 \mathrm { kPa } , N _ { \mathrm { A } } = 6.022 \times 10 ^ { 23 } \mathrm { molecules } / \mathrm { mol } \right)$

Accepted Answer

A)  $1.3 \times 10 ^ { 1 }$ 
B)  $2.7 \times 10 ^ { 1 }$ 
C)  $2.7 \times 10 ^ { 3 }$ 
D)  $1.6 \times 10 ^ { - 2 }$ 
E)  $2.7 \times 10 ^ { - 2 }$

Question 20

An oxygen molecule, $\mathrm { O } _ { 2 } ,$ falls in a vacuum. From what height must it fall so that its translational kinetic energy at the bottom of its fall equals the average translational kinetic energy of an oxygen molecule at  920 K? The mass of one $\mathrm { O } _ { 2 }$ molecule is $5.312 \times 10 ^ { - 26 } \mathrm {~kg}$ and the Boltzmann constant is $1.38 \times 10 ^ { - 23 } \mathrm {~J} / \mathrm { K }$ Neglect air resistance and assume that  g  remains constant at $9.8 \mathrm {~m} / \mathrm { s } ^ { 2 }$ throughout the fall of the molecule.

Accepted Answer

A)   5.2 km 
B)   12 km 
C)   49 km 
D)   37 km 
E)   24 km

Exam 13: Temperature and Kinetic Theory

If an ideal gas molecule has a speed of 0.50 km/s at 20∘C20 ^ { \circ } \mathrm { C }20∘C what is its speed at 80∘C?80 ^ { \circ } \mathrm { C } ?80∘C?

Nitrogen boils at −196∘C- 196 ^ { \circ } \mathrm { C }−196∘C What is the corresponding temperature in the Fahrenheit scale?

An ideal gas occupies 6.00×102 cm3 at 20∘C6.00 \times 10 ^ { 2 } \mathrm {~cm} ^ { 3 } \text { at } 20 ^ { \circ } \mathrm { C }6.00×102 cm3 at 20∘C At what temperature will it occupy 1.20×103 cm31.20 \times 10 ^ { 3 } \mathrm {~cm} ^ { 3 }1.20×103 cm3 if the pressure is held constant?

The root-mean-square speed of the molecules of an ideal gas is v. The gas is now slowly compressed to one-half its original volume with no change in temperature. What is the Root-mean-square speed of the molecules now?

Platinum melts at 3215∘F3215 ^ { \circ } \mathrm { F }3215∘F What is the corresponding temperature in the Kelvin scale?

The weather outside is frightful. The temperature is −22∘F- 22 ^ { \circ } \mathrm { F }−22∘F What is the corresponding temperature in the Celsius scale?

An ideal gas is held in a container of volume V at pressure p . The rms speed of a gas molecule under these conditions is vvv If now the volume and pressure are changed to 2 V and 2 p , the rms speed of a molecule will be

If an ideal gas molecule has a speed of 0.50 km/s at $20 ^ { \circ } \mathrm { C }$ what is its speed at $80 ^ { \circ } \mathrm { C } ?$

Nitrogen boils at $- 196 ^ { \circ } \mathrm { C }$ What is the corresponding temperature in the Fahrenheit scale?

An ideal gas occupies $6.00 \times 10 ^ { 2 } \mathrm {~cm} ^ { 3 } \text { at } 20 ^ { \circ } \mathrm { C }$ At what temperature will it occupy $1.20 \times 10 ^ { 3 } \mathrm {~cm} ^ { 3 }$ if the pressure is held constant?

Platinum melts at $3215 ^ { \circ } \mathrm { F }$ What is the corresponding temperature in the Kelvin scale?

The weather outside is frightful. The temperature is $- 22 ^ { \circ } \mathrm { F }$ What is the corresponding temperature in the Celsius scale?

An ideal gas is held in a container of volume V at pressure p . The rms speed of a gas molecule under these conditions is $v$ If now the volume and pressure are changed to 2 V and 2 p , the rms speed of a molecule will be