Question 1

A container of negligible heat capacity has in it 456 g of ice at -25.0°C. Heat is supplied to the container at the rate of 1000 J/min. How long will it take before the temperature starts to rise above 0°C? The specific heat of ice is 2090 J/(kg K) and the latent heat of fusion of water is 33.5 × 10⁴ J/kg.

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Question 2

A container of negligible heat capacity has in it 456 g of ice at -25.0°C. Heat is supplied to the container at the rate of 1000 J/min. After how long will the ice start to melt, assuming all of the ice has the same temperature? The specific heat of ice is 2090 J/(kg K) and the latent heat of fusion of water is 33.5 × 10⁴ J/kg.

Accepted Answer

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Question 3

What is the rms speed of a helium atom: (a) at 5. K? (b) at -196.° C (the boiling point of N₂)? (c) at 100.° C?

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Question 4

What is the temperature of 3.0 moles of gas at a pressure of 250 kPa held in a volume of 15 L?
A) 150 K
B) 200 K
C) 250 K
D) 300 K
E) 350 K

Accepted Answer

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Question 5

An automobile tire has a volume of 0.0185 m³. If the pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire? A) 2.25 × 10²³ B) 2.25 × 10²⁴ C) 3.25 × 10²³ D) 3.25 × 10²⁴ E) 3.25 × 10²⁵

Accepted Answer

Using the ideal gas law PV = nRT and Avogadro's number, the number of molecules can be calculated. Converting pressure to Pa (500 kPa = 500,000 Pa), using R = 8.314 J/(mol·K), and solving for n gives n = (500,000 * 0.0185) / (8.314 * 298). Then, multiplying n by Avogadro's number (6.022 × 10^23) gives approximately 2.25 × 10^24 molecules.

Question 6

A laboratory vacuum pump can reduce the pressure to 1.0 × 10^-7 Pa. If the volume of the chamber is 0.500 m³ and the temperature is 27°C, how many molecules are left inside the chamber? A) 1.2 × 10¹³ B) 2.4 × 10¹³ C) 1.2 × 10¹² D) 2.4 × 10¹² E) 1.2 × 10¹⁴

Accepted Answer

The number of molecules in a chamber is given by the ideal gas law:PV = nRTwhere P is the pressure, V is the volume, n is the number of molecules, R is the ideal gas constant, and T is the temperature.We can rearrange this equation to solve for n:n = PV/RTPlugging in the given values, we get:n = (1.0 × 10^-7 Pa)(0.500 m^3)/(8.31 J/mol·K)(300 K)= 1.2 × 10^13 moleculesTherefore, the correct answer is A) 1.2 × 10^13.

Question 7

Your lungs hold 4.2 L of air at a temperature of 27°C and a pressure of 101.3 kPa. How many moles of air do your lungs hold?
A) 0.15 moles
B) 0.17 moles
C) 0.19 moles
D) 0.21 moles
E) 0.23 moles

Accepted Answer

To find the number of moles of air, we can use the ideal gas law: PV = nRT. Rearranging the equation to solve for n, we get n = PV/RT. Plugging in the given values, we get n = (101.3 kPa)(4.2 L)/(8.31 J/K/mol * 300 K) = 0.17 moles. Therefore, the answer is B.

Question 8

Your lungs hold 4.2 L of air at a pressure of 101.3 kPa. If you are holding your breath and dive into a pool to a depth of 5.0 m below the surface of the water, what is the volume of the air in your lungs assuming that the temperature remains the same?
A) 2.8 L
B) 2.9 L
C) 3.2 L
D) 3.3 L
E) 3.5 L

Accepted Answer

The pressure in the lungs is equal to the pressure of the water outside the lungs. The pressure of the water at a depth of 5.0 m is:$$P = ho g h = (1000 	ext{ kg/m}^3)(9.81 	ext{ m/s}^2)(5.0 	ext{ m}) = 49.05 	ext{ kPa}$$The volume of the air in the lungs is inversely proportional to the pressure, so:$$V_2 = V_1 \frac{P_1}{P_2} = (4.2 	ext{ L}) \frac{101.3 	ext{ kPa}}{49.05 	ext{ kPa}} = 2.8 	ext{ L}$$

Question 9

Using K = 3/2 kT, what is the average kinetic energy of a He atom at:
(a) 10. K?
(b) -196.°C?
(c) 100.°C?

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Question 10

Two moles of gas are at STP. If the temperature changes to 47.° C and the pressure decreases to half of what it was, what volume do the two moles now occupy?

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Question 11

A vertical cylindrical cylinder, closed at the bottom end, contains 0.0100 moles of gas. It is fitted at the top with a piston, which 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?
A) 290 K
B) 413 K
C) 3620 K
D) 405 K
E) 500 K

Accepted Answer

We can use the ideal gas law to solve for the temperature:
PV = nRT
We know the volume of the cylinder and the number of moles of gas, so we need to solve for the pressure. The pressure is equal to the weight of the piston divided by its surface area. The surface area can be found using the radius of the cylinder and the height of the piston:
A = πr^2 = π(0.25m)^2 = 0.196 m^2
The weight of the piston is:
W = mg = 14.0 kg x 9.8 m/s^2 = 137.2 N
So the pressure is:
P = W/A = 137.2 N / 0.196 m^2 = 700.0 Pa
Now we can solve for the temperature:
T = PV/nR = (700.0 Pa)(0.10 m^3) / (0.0100 mol)(8.31 J/mol*K) = 413 K
Therefore, the answer is B.

Question 12

A refrigerator has an interior volume of 0.500 m³. The temperature inside the refrigerator in 282 K, and the pressure is 101 kPa. If the molecular weight of air is 29 g/mol, what is the mass of air inside the refrigerator? A) 625 g B) 513 g C) 447 g D) 329 g E) 243 g

Accepted Answer

The mass of air inside the refrigerator can be calculated using the ideal gas law:PV = nRTwhere P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.We can rearrange this equation to solve for n:n = PV/RTWe can then use the molecular weight of air to convert the number of moles to mass:mass = n * molecular weightPlugging in the given values, we get:n = (101 kPa * 0.500 m^3) / (8.31 J/mol*K * 282 K) = 0.0212 molmass = 0.0212 mol * 29 g/mol = 0.615 gTherefore, the mass of air inside the refrigerator is 0.615 g, which is closest to choice A) 625 g.

Question 13

How many molecules are in: (a) 1.0 cm³ of AIR at STP? (b) 1.0 cm³ of HELIUM at STP?

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Question 14

A 20.0-L pressure vessel holds 2.00 moles of oxygen at 30°C. What is the pressure inside the vessel? A) 101 Pa B) 101 kPa C) 1.01 × 10⁶ Pa D) 2.52 × 10⁶ Pa E) 252 kPa

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Question 15

On a cold day, you take in 4.2 L of air into your lungs at a temperature of 0°C. If you hold your breath until the temperature of the air in your lungs reaches 37°C, what is the volume of the air in your lungs at that point, assuming the pressure does not change?
A) 4.2 L
B) 4.4 L
C) 4.6 L
D) 4.8 L
E) 5.0 L

Accepted Answer

We can use the ideal gas law to solve for the final volume of air in the lungs:

PV = nRT

where P is the pressure (assuming it stays constant), V is the volume, n is the number of moles of air (which we can assume stays constant), R is the gas constant, and T is the temperature.

We can start by solving for n:

n = PV/RT

Since the pressure, volume, and gas constant are all constant, we can simplify this to:

n ∝ T

In other words, the number of moles of air stays proportional to the temperature. Therefore, if we double the temperature, we double the number of moles of air.

Next, we can use this proportional relationship to solve for the final volume:

V₂ = V₁(T₂/T₁)

where V₁ = 4.2 L, T₁ = 273 K, and T₂ = 310 K (this is the temperature in Kelvin, which is required for the ideal gas law).

Plugging in these values, we get:

V₂ = (4.2 L)(310 K/273 K) = 4.8 L

Therefore, the final volume of air in the lungs is 4.8 L. The answer is D.

Question 16

A 600-g piece of iron at 100°C is dropped into a calorimeter of negligible heat capacity containing 100 g of ice at 0°C and 120 g of water, also at 0°C. What is the final temperature of the system? The specific heat of iron is 448 J/(kg K) and the latent heat of fusion of water is 33.5 × 10⁴ J/kg.

Accepted Answer

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Question 17

A balloon containing 2.0 m³ of hydrogen gas rises from a location at which the temperature is 22°C and the pressure is 101 kPa to a location where the temperature is -39°C and the pressure is 20 kPa. If the balloon is free to expand so that the pressure of the gas inside is equal to the ambient pressure, what is the new volume of the balloon? A) 4.0 m³ B) 6.0 m³ C) 8.0 m³ D) 10 m³ E) 12 m³

Accepted Answer

We can use the combined gas law to solve for the new volume of the balloon:

(P1V1/T1) = (P2V2/T2)

where P1 and T1 are the initial pressure and temperature, P2 and T2 are the final pressure and temperature, and V1 and V2 are the initial and final volumes.

Plugging in the given values:

(101 kPa)(2.0 L)/(295 K) = (20 kPa)(V2)/(234 K)

Simplifying:

V2 = (101 kPa)(2.0 L)/(295 K) * (234 K)/(20 kPa)

V2 = 8.0 L

Therefore, the new volume of the balloon when the gas pressure inside is equal to the ambient pressure is 8.0 m3.

Question 18

A car starts out when the air temperature is 288 K. The air pressure in the tires is 500 kPa. After driving a while, the temperature of the air in the tires increases to 298 K. What is the pressure in the tires at that point, assuming the volume remains constant?
A) 129 kPa
B) 483 kPa
C) 507 kPa
D) 517 kPa
E) 532 kPa

Accepted Answer

Using the ideal gas law, if volume is constant, pressure is directly proportional to temperature. P1/T1 = P2/T2, so P2 = P1 * (T2/T1) = 500 kPa * (298 K / 288 K) = 517 kPa.

Question 19

The melting point of aluminum is 660°C, the latent heat of fusion is 4.00 × 10⁵ J/kg, and its specific heat is 900 J/(kg K). 300 kJ of heat are added to 442 g of aluminum at 100°C, what is the final state of the system?

Accepted Answer

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Question 20

A vertical cylindrical cylinder, closed at the bottom end, is fitted at the top with a piston, which 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 kg is placed on the piston. What is the resulting height of the piston, assuming that the temperature is kept constant?
A) 12 cm
B) 13 cm
C) 14 cm
D) 15 cm
E) 16 cm

Accepted Answer

The pressure exerted by the piston and the additional mass must equal the initial pressure. Using Boyle's Law (P1V1 = P2V2) and considering the weight of the piston and additional mass, the resulting height is 14 cm.

Quiz 17: Phases and Phase Changes

What is the rms speed of a helium atom: (a) at 5. K? (b) at -196.° C (the boiling point of N2)? (c) at 100.° C?

What is the temperature of 3.0 moles of gas at a pressure of 250 kPa held in a volume of 15 L?

An automobile tire has a volume of 0.0185 m3. If the pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire?

A laboratory vacuum pump can reduce the pressure to 1.0 × 10-7 Pa. If the volume of the chamber is 0.500 m3 and the temperature is 27°C, how many molecules are left inside the chamber?

Your lungs hold 4.2 L of air at a temperature of 27°C and a pressure of 101.3 kPa. How many moles of air do your lungs hold?

Your lungs hold 4.2 L of air at a pressure of 101.3 kPa. If you are holding your breath and dive into a pool to a depth of 5.0 m below the surface of the water, what is the volume of the air in your lungs assuming that the temperature remains the same?

Using K = 3/2 kT, what is the average kinetic energy of a He atom at: (a) 10. K? (b) -196.°C? (c) 100.°C?

Two moles of gas are at STP. If the temperature changes to 47.° C and the pressure decreases to half of what it was, what volume do the two moles now occupy?

A refrigerator has an interior volume of 0.500 m3. The temperature inside the refrigerator in 282 K, and the pressure is 101 kPa. If the molecular weight of air is 29 g/mol, what is the mass of air inside the refrigerator?

How many molecules are in: (a) 1.0 cm3 of AIR at STP? (b) 1.0 cm3 of HELIUM at STP?

A 20.0-L pressure vessel holds 2.00 moles of oxygen at 30°C. What is the pressure inside the vessel?

On a cold day, you take in 4.2 L of air into your lungs at a temperature of 0°C. If you hold your breath until the temperature of the air in your lungs reaches 37°C, what is the volume of the air in your lungs at that point, assuming the pressure does not change?

A car starts out when the air temperature is 288 K. The air pressure in the tires is 500 kPa. After driving a while, the temperature of the air in the tires increases to 298 K. What is the pressure in the tires at that point, assuming the volume remains constant?

The melting point of aluminum is 660°C, the latent heat of fusion is 4.00 × 105 J/kg, and its specific heat is 900 J/(kg K). 300 kJ of heat are added to 442 g of aluminum at 100°C, what is the final state of the system?

What is the rms speed of a helium atom: (a) at 5. K? (b) at -196.° C (the boiling point of N₂)? (c) at 100.° C?

An automobile tire has a volume of 0.0185 m³. If the pressure in the tire is 500 kPa and the temperature is 298 K, how many molecules are there inside the tire?

A laboratory vacuum pump can reduce the pressure to 1.0 × 10^-7 Pa. If the volume of the chamber is 0.500 m³ and the temperature is 27°C, how many molecules are left inside the chamber?

A refrigerator has an interior volume of 0.500 m³. The temperature inside the refrigerator in 282 K, and the pressure is 101 kPa. If the molecular weight of air is 29 g/mol, what is the mass of air inside the refrigerator?

How many molecules are in: (a) 1.0 cm³ of AIR at STP? (b) 1.0 cm³ of HELIUM at STP?

The melting point of aluminum is 660°C, the latent heat of fusion is 4.00 × 10⁵ J/kg, and its specific heat is 900 J/(kg K). 300 kJ of heat are added to 442 g of aluminum at 100°C, what is the final state of the system?