Question 1

The pressures p and volumes V of the five ideal gases,with the same number of molecules, are given below. Which has the highest theperatures?

Accepted Answer

B

Question 2

A sample of an ideal gas is compressed by a piston from 10 m³ to 5 m³ and simultaneously cooled from 273 $\degree$C to 0 $\degree$C. As a result there is:

Accepted Answer

E

Question 3

A 2-m³ weather balloon is loosely filled with helium at 1 atm (76 cm Hg) and at 27 $\degree$C. At an elevation of 20,000 ft, the atmospheric pressure is down to 38 cm Hg and the helium has expanded, being under no constraint from the confining bag. If the temperature at this elevation is -48 $\degree$C, the gas volume (in m³) is:

Accepted Answer

A

Question 4

A given mass of gas is enclosed in a suitable container so that it may be maintained at constant volume. Under these conditions, there can be no change is what property of the gas?

Accepted Answer

The answer of A given mass of gas is enclosed...

Question 5

In order that a single process be both isothermal and isobaric:

Accepted Answer

For a single process to be both isothermal and isobaric, a change of phase is essential. This is because during the phase change, the temperature remains constant (isothermal) and the pressure also remains constant (isobaric). For example, the process of boiling water at atmospheric pressure can be considered as an isothermal and isobaric process.

Question 6

An automobile tire is pumped up to a gauge pressure of 2.0 * 10⁵ Pa when the temperature is 27 $\degree$C. What is its gauge pressure after the car has been running on a hot day so that the tire temperature is 77 $\degree$C? Assume that the volume remains fixed and take atmospheric pressure to be 1.013 * 10⁵ Pa.

Accepted Answer

The answer of An automobile tire is pumped up to...

Question 7

A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest.

Accepted Answer

The answer of A quantity of an ideal gas is...

Question 8

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m³). Ignoring any temperature changes, the depth of the lake is:

Accepted Answer

The answer of An air bubble doubles in volume as...

Question 9

Oxygen (molar mass = 32 g) occupies a volume of 12 liters when its temperature is 20$\degree$C and its pressure is 1 atm. Using R = 0.082 liter. atm/mole . K, calculate the mass of the oxygen:

Accepted Answer

First, we need to convert the temperature from Celsius to Kelvin: 
20°C + 273.15 = 293.15 K

Then, we can use the ideal gas law: 
PV = nRT

where P = pressure, V = volume, n = number of moles, R = gas constant, and T = temperature in Kelvin.

We can solve for n (number of moles): 
n = PV/RT

Plugging in the values: 
n = (1 atm)(12 L)/(0.082 L atm/mol K)(293.15 K) 
n = 0.492 mol

Finally, we can calculate the mass using the molar mass: 
mass = n x molar mass 
mass = 0.492 mol x 32 g/mol 
mass = 15.744 g

Rounding to one significant figure, the answer is 16 g.

Question 10

An isothermal process for an ideal gas is represented on a p-V diagram by:

Accepted Answer

An isothermal process for an ideal gas is represented by a hyperbola on a p-V diagram, according to the ideal gas law PV = nRT, where P is pressure, V is volume, n is the amount of substance, R is the ideal gas constant, and T is temperature. In an isothermal process, the temperature (T) remains constant, so the product of pressure (P) and volume (V) remains constant, resulting in a hyperbolic curve.

Question 11

An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg). Its temperature is now raised to 373 K and its pressure increased to 215 cm Hg. The new volume is:

Accepted Answer

The answer of An ideal gas occupies 12 liters at...

Question 12

273 cm³ of an ideal gas is at 0 $\degree$C. It is heated at constant pressure to 10 $\degree$C. It will now occupy:

Accepted Answer

According to Charles's law, the volume of an ideal gas is directly proportional to its absolute temperature, assuming constant pressure. The temperature change in this scenario is from 273K (0°C + 273) to 283K (10°C + 273), which is a 10K increase. Therefore, the volume of the gas will also increase proportionally. Since the initial volume is given as 273 cm3, the final volume can be calculated as:
V2 = V1 * (T2/T1)
V2 = 273 * (283/273) = 283 cm3
Thus, the gas will now occupy 283 cm3, and the answer is choice C.

Question 13

An ideal gas undergoes an isothermal process starting with a pressure of 2* 10⁵ Pa and a volume of 6 cm³. Which of the following might be the pressure and volume of the final state?

Accepted Answer

In an isothermal process, the temperature remains constant. Therefore, we can use the ideal gas law to find the final pressure and volume:

P1V1 = P2V2

where P1 = 2 x 10^5 Pa, V1 = 6 cm^3, and P2 and V2 are the final pressure and volume, respectively. Since the process is isothermal, we can also use the equation PV = nRT, where n is the number of moles of gas, R is the gas constant, and T is the temperature.

Setting the initial and final states equal, we have:

P1V1 = nRT

and

P2V2 = nRT

Dividing the second equation by the first, we get:

P2/P1 = V1/V2

Substituting the values we have:

P2/2 x 10^5 Pa = 6 cm^3/V2

P2V2 = 12 x 10^5 cm^3 Pa

Now, we can use the ideal gas law to find the final volume:

PV = nRT

Substituting P2 = 6 x 10^5 Pa, V2 = ?, and the other values:

6 x 10^5 Pa x V2 = n x R x T

Since the process is isothermal, T remains constant. Therefore, we can write:

6 x 10^5 Pa x V2 = n x R x T1

where T1 is the initial temperature.

We can simplify this equation using the fact that for an ideal gas, PV = nRT:

6 x 10^5 Pa x V2 = P1V1

Substituting the values we have:

6 x 10^5 Pa x V2 = 2 x 10^5 Pa x 6 cm^3

V2 = 2 cm^3

Therefore, the final state is:

Pressure = 6 x 10^5 Pa
Volume = 2 cm^3

The answer is choice D.

Question 14

Two identical rooms in a house are connected by an open doorway. The temperatures in the two rooms are maintained at different values. Which room contains more air?

Accepted Answer

According to the ideal gas law, the volume of a gas is directly proportional to its temperature at constant pressure. Therefore, the room with the higher temperature has more expanded air and therefore less air molecules than the other room with the lower temperature. Consequently, the room with the lower temperature contains more air.

Question 15

A real gas undergoes a process which can be represented as a curve on a p-V diagram. The work done by the gas during this process is:

Accepted Answer

The work done by a gas during a process represented on a p-V diagram is given by the area under the curve on the diagram, which is mathematically represented by the integral of pressure with respect to volume, or $\int p dV$. This corresponds to choice D.

Question 16

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$C, 1 atm). The volume occupied by 42 grams of this gas at standard conditions is:

Accepted Answer

The amount of gas (in moles) is directly proportional to its mass. Therefore, 42 grams of this gas is equivalent to 1.5 times the amount of gas that occupies 28 grams. Since the volume is also directly proportional to the amount of gas, the volume occupied by 42 grams of this gas would be 1.5 times the volume occupied by 28 grams.

Calculation: 
(42 g / 28 g) = 1.5
1.5 x 22.4 L = 33.6 L

Therefore, the answer is C) 33.6 liters.

Question 17

Over 1 cycle of a cyclic process in which a system does net work on its environment:

Accepted Answer

In a cyclic process, the system returns to its initial state at the end of the cycle. This means that all state functions, including pressure, volume, temperature, and internal energy, return to their initial values. Therefore, the changes in these properties over one complete cycle are zero.

Question 18

A real gas is changed slowly from state 1 to state 2. During this process no work is done on or by the gas. This process must be:

Accepted Answer

The answer of A real gas is changed slowly from...

Question 19

Air enters a hot-air furnace at 7 $\degree$C and leaves at 77 $\degree$C. If the pressure does not change each entering cubic foot of air expands to:

Accepted Answer

The answer of Air enters a hot-air furnace at 7...

Question 20

Use R = 8.2 * 10^-⁵ m³ .atm/mol.K and N_A = 6.02 * 10²³ mol^-¹. The approximate number of air molecules in a 1 m³ volume at room temperature (300 K) and atomospheric pressure is:

Accepted Answer

Using the ideal gas law, we can find the number of moles of air in a 1 m3 volume at room temperature and atmospheric pressure: PV = nRT n = PV/RT P = 1 atm = 1.01325 × 105 Pa V = 1 m3 n = (1.01325 × 105 Pa)(1 m3)/(8.314 J/(mol·K) × 300 K) = 40.7 mol Since there are N_A = 6.02 F1F1F1S1F1F1F10 10²³ molecules per mole, the number of air molecules is: (40.7 mol)(6.02 F1F1F1S1F1F1F10 10²³ molecules/mol) = 2.45 F1F1F1S1F1F1F10 10²⁵ molecules Therefore, the best choice is C.

Quiz 19: The Kinetic Theory of Gases

The pressures p and volumes V of the five ideal gases,with the same number of molecules, are given below. Which has the highest theperatures?

A sample of an ideal gas is compressed by a piston from 10 m³ to 5 m³ and simultaneously cooled from 273 $\degree$ C to 0 $\degree$ C. As a result there is:

A given mass of gas is enclosed in a suitable container so that it may be maintained at constant volume. Under these conditions, there can be no change is what property of the gas?

In order that a single process be both isothermal and isobaric:

A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest.

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m³) . Ignoring any temperature changes, the depth of the lake is:

Oxygen (molar mass = 32 g) occupies a volume of 12 liters when its temperature is 20 $\degree$ C and its pressure is 1 atm. Using R = 0.082 liter. atm/mole . K, calculate the mass of the oxygen:

An isothermal process for an ideal gas is represented on a p-V diagram by:

An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg) . Its temperature is now raised to 373 K and its pressure increased to 215 cm Hg. The new volume is:

273 cm³ of an ideal gas is at 0 $\degree$ C. It is heated at constant pressure to 10 $\degree$ C. It will now occupy:

An ideal gas undergoes an isothermal process starting with a pressure of 2* 10⁵ Pa and a volume of 6 cm³. Which of the following might be the pressure and volume of the final state?

Two identical rooms in a house are connected by an open doorway. The temperatures in the two rooms are maintained at different values. Which room contains more air?

A real gas undergoes a process which can be represented as a curve on a p-V diagram. The work done by the gas during this process is:

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$ C, 1 atm) . The volume occupied by 42 grams of this gas at standard conditions is:

Over 1 cycle of a cyclic process in which a system does net work on its environment:

A real gas is changed slowly from state 1 to state 2. During this process no work is done on or by the gas. This process must be:

Air enters a hot-air furnace at 7 $\degree$ C and leaves at 77 $\degree$ C. If the pressure does not change each entering cubic foot of air expands to:

Use R = 8.2 * 10^-⁵ m³ .atm/mol.K and N_A = 6.02 * 10²³ mol^-¹. The approximate number of air molecules in a 1 m³ volume at room temperature (300 K) and atomospheric pressure is:

Quiz 19: The Kinetic Theory of Gases

The pressures p and volumes V of the five ideal gases,with the same number of molecules, are given below. Which has the highest theperatures?

A sample of an ideal gas is compressed by a piston from 10 m3 to 5 m3 and simultaneously cooled from 273 °\degree° C to 0 °\degree° C. As a result there is:

A given mass of gas is enclosed in a suitable container so that it may be maintained at constant volume. Under these conditions, there can be no change is what property of the gas?

In order that a single process be both isothermal and isobaric:

A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest.

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m3) . Ignoring any temperature changes, the depth of the lake is:

Oxygen (molar mass = 32 g) occupies a volume of 12 liters when its temperature is 20 °\degree° C and its pressure is 1 atm. Using R = 0.082 liter. atm/mole . K, calculate the mass of the oxygen:

An isothermal process for an ideal gas is represented on a p-V diagram by:

An ideal gas occupies 12 liters at 293 K and 1 atm (76 cm Hg) . Its temperature is now raised to 373 K and its pressure increased to 215 cm Hg. The new volume is:

273 cm3 of an ideal gas is at 0 °\degree° C. It is heated at constant pressure to 10 °\degree° C. It will now occupy:

An ideal gas undergoes an isothermal process starting with a pressure of 2* 105 Pa and a volume of 6 cm3. Which of the following might be the pressure and volume of the final state?

Two identical rooms in a house are connected by an open doorway. The temperatures in the two rooms are maintained at different values. Which room contains more air?

A real gas undergoes a process which can be represented as a curve on a p-V diagram. The work done by the gas during this process is:

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 °\degree° C, 1 atm) . The volume occupied by 42 grams of this gas at standard conditions is:

Over 1 cycle of a cyclic process in which a system does net work on its environment:

A real gas is changed slowly from state 1 to state 2. During this process no work is done on or by the gas. This process must be:

Air enters a hot-air furnace at 7 °\degree° C and leaves at 77 °\degree° C. If the pressure does not change each entering cubic foot of air expands to:

Use R = 8.2 * 10-5 m3 .atm/mol.K and NA = 6.02 * 1023 mol-1. The approximate number of air molecules in a 1 m3 volume at room temperature (300 K) and atomospheric pressure is:

A sample of an ideal gas is compressed by a piston from 10 m³ to 5 m³ and simultaneously cooled from 273 $\degree$ C to 0 $\degree$ C. As a result there is:

An air bubble doubles in volume as it rises from the bottom of a lake (1000 kg/m³) . Ignoring any temperature changes, the depth of the lake is:

Oxygen (molar mass = 32 g) occupies a volume of 12 liters when its temperature is 20 $\degree$ C and its pressure is 1 atm. Using R = 0.082 liter. atm/mole . K, calculate the mass of the oxygen:

273 cm³ of an ideal gas is at 0 $\degree$ C. It is heated at constant pressure to 10 $\degree$ C. It will now occupy:

An ideal gas undergoes an isothermal process starting with a pressure of 2* 10⁵ Pa and a volume of 6 cm³. Which of the following might be the pressure and volume of the final state?

It is known that 28 grams of a certain ideal gas occupy 22.4 liters at standard conditions (0 $\degree$ C, 1 atm) . The volume occupied by 42 grams of this gas at standard conditions is:

Air enters a hot-air furnace at 7 $\degree$ C and leaves at 77 $\degree$ C. If the pressure does not change each entering cubic foot of air expands to:

Use R = 8.2 * 10^-⁵ m³ .atm/mol.K and N_A = 6.02 * 10²³ mol^-¹. The approximate number of air molecules in a 1 m³ volume at room temperature (300 K) and atomospheric pressure is: