Question 1

The pressure of an ideal gas is tripled and its volume is decreased to 25% of its original value.How is the temperature affected?

Accepted Answer

The answer of The pressure of an ideal gas is...

Question 2

One hundred grams of liquid argon is sealed inside of a 2.0 liter container.After the liquid argon turns into a gas and the gas reaches a temperature of 0.0 degrees Celsius,what is the pressure inside the container due to the liquid argon?

Accepted Answer

The pressure can be calculated using the ideal gas law, PV = nRT. First, convert 100 grams of argon to moles (100 g / 39.95 g/mol ≈ 2.5 mol). Use R = 0.0821 L·atm/mol·K and T = 273 K. Solving for P gives P = (2.5 mol * 0.0821 L·atm/mol·K * 273 K) / 2.0 L ≈ 28 atm.

Question 3

There are two vessels;one contains twice as many molecules as the other but has the same volume.

Accepted Answer

According to the ideal gas law (PV=nRT), if two vessels have the same volume and pressure, the one with more molecules (higher n) must have a lower temperature to maintain the equality, specifically half the temperature if it has twice the molecules.

Question 4

A scuba diver at a depth of 20 m exhales,releasing a spherical bubble of gas.The bubble floats towards the surface maintaining its spherical shape.When the bubble is 1.0 m below the surface,its diameter is 17 cm.What was the diameter of the air bubble just as it left the diver?

Accepted Answer

The answer of A scuba diver at a depth of...

Question 5

A piston with a volume of 24 liters contains 3.0 moles of argon.It is heated from 20 degrees Celsius to 178 degrees Celsius,and the piston is allowed to expand during the heating process so that the pressure on the gas remains constant.How much heat must be added to the gas to heat it?

Accepted Answer

First, we need to convert the temperature to Kelvin by adding 273.15 to each temperature. So the initial temperature is 293.15 K and the final temperature is 451.15 K. Since the pressure remains constant, we can use the formula Q = nCpΔT, where n is the number of moles, Cp is the molar heat capacity at constant pressure, and ΔT is the change in temperature. 
Using the molar heat capacity of argon at constant pressure (Cp = 20.8 J/mol*K), we get: 
Q = 3.0 mol * 20.8 J/mol*K * (451.15 K - 293.15 K) = 9900 J
Therefore, the answer is C.

Question 6

Air in an engine cylinder is quickly compressed from an initial temperature of 10S1U1P1$\circ$S1S1P0C,an initial pressure of 1.0 atmosphere,and an initial volume of 250 cm³ to a final volume of 30 cm³.Assuming the air to be an ideal diatomic gas,find the final temperature of the air.

Accepted Answer

To find the final temperature of the air in the engine cylinder, we can use the ideal gas law and the concept of adiabatic compression. For an adiabatic process involving an ideal diatomic gas, the equation relating the initial and final states is $T_2 = T_1 \left(\frac{V_1}{V_2}\right)^{\gamma-1}$, where $\gamma = \frac{C_p}{C_v} = \frac{7}{5}$ for a diatomic gas. Given $T_1 = 10^\circ C = 283 K$, $V_1 = 250 \, \text{cm}^3$, and $V_2 = 30 \, \text{cm}^3$, we can calculate $T_2$. Converting the final temperature back to Celsius gives a result close to 390°C, indicating that choice B is correct.

Question 7

A scuba diver exhales,releasing a spherical bubble of gas with a diameter of 10 cm.The bubble floats towards the surface maintaining its spherical shape.When the bubble is 1.0 m below the surface,its diameter is 16 cm.How far below the water's surface is the diver?

Accepted Answer

We can use the equation PV = k, where P is pressure, V is volume and k is a constant. Since the bubble floats towards the surface, the pressure inside the bubble is equal to the pressure outside the bubble when it is at the surface. Let's call this pressure P0. When the bubble is 1.0 m below the surface, the pressure inside the bubble is equal to the pressure at that depth, let's call this pressure P1. Since the bubble maintains its spherical shape, we can use the equation for the volume of a sphere:
V = (4/3)πr^3

When the bubble is at the surface, its diameter is 10 cm, so its radius is 5 cm. Therefore, its volume is:
V0 = (4/3)π(5 cm)^3 = 523.6 cm^3

When the bubble is 1.0 m below the surface, its diameter is 16 cm, so its radius is 8 cm. Therefore, its volume is:
V1 = (4/3)π(8 cm)^3 = 2144 cm^3

Since PV is constant, we have:
P0V0 = P1V1

We can solve for P0:
P0 = P1V1/V0 = (1 atm)(2144 cm^3)/(523.6 cm^3) = 4.08 atm

We can use the equation for pressure in a fluid:
P = ρgh

Where ρ is the density of water (1000 kg/m^3), g is the acceleration due to gravity (9.81 m/s^2), and h is the depth below the surface. Solving for h, we get:
h = P/(ρg) = (4.08 atm)(101325 Pa/atm)/(1000 kg/m^3)(9.81 m/s^2) = 36.9 m

Therefore, the diver is 36.9 m below the water's surface. 
The best choice is B, 36 m.

Question 8

Two moles of helium are initially at 23S1U1P1$\circ$S1S1P0C and 1 atm.The work done by the gas at constant pressure when the volume is doubled is

Accepted Answer

The work done at constant pressure can be given by the formula:
W = -PΔV
where ΔV is the change in volume and P is the pressure.
Initially, the volume of 2 moles of helium is V1 = nRT/P = (2 mol)(0.0821 L atm/K mol)(23°C + 273.15)/1 atm = 98.96 L
When the volume is doubled, the new volume is V2 = 2V1 = 197.92 L
Therefore, the change in volume is ΔV = V2 - V1 = 98.96 L
Since the pressure is constant at 1 atm, the work done is:
W = -PΔV = -(1 atm)(98.96 L) = -98.96 L atm
Converting to joules using the conversion factor 1 L atm = 101.325 J, we get:
W = -98.96 L atm x 101.325 J/L atm = -10020.9 J
Rounding to two significant figures, we get the answer:
W = -4.92 kJ (since the work done is negative, we take the absolute value and express it in kilojoules)

Question 9

A sealed glass bottle containing air at atmospheric pressure is tossed into an open fire.Assuming that no air escapes,and that the bottle's deformation is negligible,which of the following diagrams best describes the changes of the conditions of the air inside the bottle?

Accepted Answer

The answer of A sealed glass bottle containing air at...

Question 10

The temperature of an ideal gas is doubled (in K)and its volume is decreased to 25% of its original value.How is the pressure affected?

Accepted Answer

The pressure of an ideal gas is directly proportional to its temperature (in Kelvin) and inversely proportional to its volume. If the temperature is doubled and the volume is decreased to 25% (or 1/4) of its original value, the pressure would increase by a factor of 2 (due to temperature doubling) and by a factor of 4 (due to volume reduction to 1/4), resulting in an overall increase by a factor of 8. Therefore, P' = 8P.

Question 11

Two containers of equal volume contain different ideal gases at the same temperature and pressure.It follows that

Accepted Answer

According to Avogadro's Law, equal volumes of gases at the same temperature and pressure contain the same number of molecules. Therefore, both containers hold the same number of molecules.

Question 12

If a gas is in equilibrium at 19S1U1P1$\circ$S1S1P0C and is then heated to 38S1U1P1$\circ$S1S1P0C,what is the ratio of the average molecular speed to its previous value?

Accepted Answer

The average molecular speed of a gas is proportional to the square root of its absolute temperature (in Kelvin). When the temperature is increased from 19°C to 38°C, we first convert these temperatures to Kelvin (by adding 273) to get 292K and 311K, respectively. The ratio of the speeds is then the square root of the ratio of the temperatures, which is $\sqrt{\frac{311}{292}}$, matching choice (C).

Question 13

What is the rms speed for a collection of helium-3 atoms at 47 degrees Celsius in a container with a volume of 5.0 liters?

Accepted Answer

The answer of What is the rms speed for a...

Question 14

A diesel engine takes in air ($\gamma$ = 1.4)at 20S1U1P1$\circ$S1S1P0C and compresses it adiabatically to 1/10 of its original volume.The final temperature of the air is

Accepted Answer

Using the adiabatic compression formula:

(P1/P2)^((γ-1)/γ) = (T2/T1)

where P is pressure and T is temperature, and γ is the ratio of specific heats.

Firstly, convert the temperature in Celsius to Kelvin:

T1 = 20°C + 273.15 = 293.15 K

Since the compression ratio is 1/10, the final pressure is 10 times the initial pressure:

P2 = 10P1

Plugging in the values, we get:

(10)^((1.4-1)/1.4) = (T2/293.15)

Simplifying, we get:

T2 = 463.15 K

Therefore, the final temperature is 463°F.

Question 15

1.5 liters of nitrogen at 112S1U1P1$\circ$S1S1P0C and 2.8 atmospheres contain how many moles?

Accepted Answer

To find the number of moles, use the ideal gas law: PV = nRT. Here, P = 2.8 atm, V = 1.5 L, R = 0.0821 L·atm/mol·K, and T = 112°C = 385 K. Solving for n gives approximately 0.13 moles.

Question 16

If,while the temperature is kept constant,the pressure of a diatomic gas doubles,the average kinetic energy of the molecules

Accepted Answer

The average kinetic energy of gas molecules is directly proportional to the temperature of the gas (according to the kinetic theory of gases). If the temperature is kept constant, the average kinetic energy of the molecules remains the same, regardless of changes in pressure.

Question 17

A cylindrical drinking glass with diameter 8.6 cm and height 25 cm is inverted and carefully lowered into a tank of water.If no air is allowed to escape from the glass as it is submerged,what is the height of the air column in the glass when the glass is 2.0 m below the surface of the water?

Accepted Answer

The pressure at 2.0 m below the surface can be calculated using the formula $P = P_0 + \rho gh$, where $P_0$ is the atmospheric pressure, $\rho$ is the density of water (1000 kg/m³), $g$ is the acceleration due to gravity (9.8 m/s²), and $h$ is the depth (2.0 m). The pressure inside the glass must equal the pressure outside for no air to escape. Initially, the volume of air is the volume of the cylinder, and finally, it's the volume of a smaller cylinder with the same diameter but unknown height. Using Boyle's Law, $P_1V_1 = P_2V_2$, and knowing the initial and final pressures and the initial volume, we can solve for the final volume and thus the height of the air column. Given the diameter (8.6 cm), we can find the radius (4.3 cm) and use it to calculate the initial volume. The final pressure is the sum of atmospheric pressure and the pressure due to the water column above the glass. With these values, we can find the final volume and thus the height of the air column, which is 20.9 cm.

Question 18

A scuba diver at a depth of 20 m exhales,releasing a spherical bubble of gas with a diameter of 10 cm.The bubble floats towards the surface and assuming that it maintains its spherical shape,what is its diameter when it is 1.0 m below the surface?

Accepted Answer

The pressure at a depth of 20 m is higher than at a depth of 1.0 m. As the bubble rises towards the surface, the pressure around it decreases and its volume increases. However, we are assuming that it maintains its spherical shape, which means that its radius must increase by a constant factor.

The pressure at a depth of 20 m is approximately 3 times higher than at a depth of 1.0 m (assuming that the density of water is constant). This means that the volume of the bubble should increase by a factor of 3 as it rises towards the surface.

The volume of a sphere is given by the formula: V = (4/3)πr^3. If the volume increases by a factor of 3, then the radius must increase by a factor of cube root of 3.

The diameter of the bubble at a depth of 1.0 m is therefore:

d = 2r = 2(10 cm) x cube root of 3 ≈ 14 cm.

Therefore, the best choice is D) 14 cm.

Question 19

Which of the following statements is true about the average speed of an oxygen molecule,O₂,and that of a N₂ molecule in a gas at fixed temperature and pressure? M_O =16,M_N =14

Accepted Answer

The average speed of gas molecules at a given temperature is inversely proportional to the square root of their molar mass. Since the molar mass of $O_2$ (32 g/mol) is greater than that of $N_2$ (28 g/mol), the average speed of $N_2$ molecules will be higher. The correct ratio of their speeds is given by the square root of the inverse ratio of their masses, which is $\sqrt{\frac{28}{32}}$ or $\frac{28}{32}^{1/2}$.

Question 20

The cylinder shown has a radius of 6.0 cm.The current pressure of the gas inside is 2.0 atm.The piston is then pushed in by 20 cm,which is 1/3 of the length of the cylinder.If the temperature remains constant,what is the new pressure of the gas?

Accepted Answer

The answer of The cylinder shown has a radius of...

Quiz 19: Ideal Gases

The pressure of an ideal gas is tripled and its volume is decreased to 25% of its original value.How is the temperature affected?

One hundred grams of liquid argon is sealed inside of a 2.0 liter container.After the liquid argon turns into a gas and the gas reaches a temperature of 0.0 degrees Celsius,what is the pressure inside the container due to the liquid argon?

There are two vessels;one contains twice as many molecules as the other but has the same volume.

A scuba diver at a depth of 20 m exhales,releasing a spherical bubble of gas.The bubble floats towards the surface maintaining its spherical shape.When the bubble is 1.0 m below the surface,its diameter is 17 cm.What was the diameter of the air bubble just as it left the diver?

A piston with a volume of 24 liters contains 3.0 moles of argon.It is heated from 20 degrees Celsius to 178 degrees Celsius,and the piston is allowed to expand during the heating process so that the pressure on the gas remains constant.How much heat must be added to the gas to heat it?

Air in an engine cylinder is quickly compressed from an initial temperature of 10^$\circ$C,an initial pressure of 1.0 atmosphere,and an initial volume of 250 cm³ to a final volume of 30 cm³.Assuming the air to be an ideal diatomic gas,find the final temperature of the air.

A scuba diver exhales,releasing a spherical bubble of gas with a diameter of 10 cm.The bubble floats towards the surface maintaining its spherical shape.When the bubble is 1.0 m below the surface,its diameter is 16 cm.How far below the water's surface is the diver?

Two moles of helium are initially at 23^$\circ$C and 1 atm.The work done by the gas at constant pressure when the volume is doubled is

A sealed glass bottle containing air at atmospheric pressure is tossed into an open fire.Assuming that no air escapes,and that the bottle's deformation is negligible,which of the following diagrams best describes the changes of the conditions of the air inside the bottle?

The temperature of an ideal gas is doubled (in K) and its volume is decreased to 25% of its original value.How is the pressure affected?

Two containers of equal volume contain different ideal gases at the same temperature and pressure.It follows that

If a gas is in equilibrium at 19^$\circ$C and is then heated to 38^$\circ$C,what is the ratio of the average molecular speed to its previous value?

What is the rms speed for a collection of helium-3 atoms at 47 degrees Celsius in a container with a volume of 5.0 liters?

A diesel engine takes in air ( $\gamma$ = 1.4) at 20^$\circ$C and compresses it adiabatically to 1/10 of its original volume.The final temperature of the air is

1.5 liters of nitrogen at 112^$\circ$C and 2.8 atmospheres contain how many moles?

If,while the temperature is kept constant,the pressure of a diatomic gas doubles,the average kinetic energy of the molecules

A cylindrical drinking glass with diameter 8.6 cm and height 25 cm is inverted and carefully lowered into a tank of water.If no air is allowed to escape from the glass as it is submerged,what is the height of the air column in the glass when the glass is 2.0 m below the surface of the water?

A scuba diver at a depth of 20 m exhales,releasing a spherical bubble of gas with a diameter of 10 cm.The bubble floats towards the surface and assuming that it maintains its spherical shape,what is its diameter when it is 1.0 m below the surface?

Which of the following statements is true about the average speed of an oxygen molecule,O₂,and that of a N₂ molecule in a gas at fixed temperature and pressure? M_O =16,M_N =14

The cylinder shown has a radius of 6.0 cm.The current pressure of the gas inside is 2.0 atm.The piston is then pushed in by 20 cm,which is 1/3 of the length of the cylinder.If the temperature remains constant,what is the new pressure of the gas?

Quiz 19: Ideal Gases

The pressure of an ideal gas is tripled and its volume is decreased to 25% of its original value.How is the temperature affected?

One hundred grams of liquid argon is sealed inside of a 2.0 liter container.After the liquid argon turns into a gas and the gas reaches a temperature of 0.0 degrees Celsius,what is the pressure inside the container due to the liquid argon?

There are two vessels;one contains twice as many molecules as the other but has the same volume.

A scuba diver at a depth of 20 m exhales,releasing a spherical bubble of gas.The bubble floats towards the surface maintaining its spherical shape.When the bubble is 1.0 m below the surface,its diameter is 17 cm.What was the diameter of the air bubble just as it left the diver?

A piston with a volume of 24 liters contains 3.0 moles of argon.It is heated from 20 degrees Celsius to 178 degrees Celsius,and the piston is allowed to expand during the heating process so that the pressure on the gas remains constant.How much heat must be added to the gas to heat it?

Air in an engine cylinder is quickly compressed from an initial temperature of 10 ∘\circ∘ C,an initial pressure of 1.0 atmosphere,and an initial volume of 250 cm3 to a final volume of 30 cm3.Assuming the air to be an ideal diatomic gas,find the final temperature of the air.

A scuba diver exhales,releasing a spherical bubble of gas with a diameter of 10 cm.The bubble floats towards the surface maintaining its spherical shape.When the bubble is 1.0 m below the surface,its diameter is 16 cm.How far below the water's surface is the diver?

Two moles of helium are initially at 23 ∘\circ∘ C and 1 atm.The work done by the gas at constant pressure when the volume is doubled is

A sealed glass bottle containing air at atmospheric pressure is tossed into an open fire.Assuming that no air escapes,and that the bottle's deformation is negligible,which of the following diagrams best describes the changes of the conditions of the air inside the bottle?

The temperature of an ideal gas is doubled (in K) and its volume is decreased to 25% of its original value.How is the pressure affected?

Two containers of equal volume contain different ideal gases at the same temperature and pressure.It follows that

If a gas is in equilibrium at 19 ∘\circ∘ C and is then heated to 38 ∘\circ∘ C,what is the ratio of the average molecular speed to its previous value?

What is the rms speed for a collection of helium-3 atoms at 47 degrees Celsius in a container with a volume of 5.0 liters?

A diesel engine takes in air ( γ\gammaγ = 1.4) at 20 ∘\circ∘ C and compresses it adiabatically to 1/10 of its original volume.The final temperature of the air is

1.5 liters of nitrogen at 112 ∘\circ∘ C and 2.8 atmospheres contain how many moles?

If,while the temperature is kept constant,the pressure of a diatomic gas doubles,the average kinetic energy of the molecules

A cylindrical drinking glass with diameter 8.6 cm and height 25 cm is inverted and carefully lowered into a tank of water.If no air is allowed to escape from the glass as it is submerged,what is the height of the air column in the glass when the glass is 2.0 m below the surface of the water?

A scuba diver at a depth of 20 m exhales,releasing a spherical bubble of gas with a diameter of 10 cm.The bubble floats towards the surface and assuming that it maintains its spherical shape,what is its diameter when it is 1.0 m below the surface?

Which of the following statements is true about the average speed of an oxygen molecule,O2,and that of a N2 molecule in a gas at fixed temperature and pressure? MO =16,MN =14

The cylinder shown has a radius of 6.0 cm.The current pressure of the gas inside is 2.0 atm.The piston is then pushed in by 20 cm,which is 1/3 of the length of the cylinder.If the temperature remains constant,what is the new pressure of the gas?

Air in an engine cylinder is quickly compressed from an initial temperature of 10^$\circ$C,an initial pressure of 1.0 atmosphere,and an initial volume of 250 cm³ to a final volume of 30 cm³.Assuming the air to be an ideal diatomic gas,find the final temperature of the air.

Two moles of helium are initially at 23^$\circ$C and 1 atm.The work done by the gas at constant pressure when the volume is doubled is

If a gas is in equilibrium at 19^$\circ$C and is then heated to 38^$\circ$C,what is the ratio of the average molecular speed to its previous value?

A diesel engine takes in air ( $\gamma$ = 1.4) at 20^$\circ$C and compresses it adiabatically to 1/10 of its original volume.The final temperature of the air is

1.5 liters of nitrogen at 112^$\circ$C and 2.8 atmospheres contain how many moles?

Which of the following statements is true about the average speed of an oxygen molecule,O₂,and that of a N₂ molecule in a gas at fixed temperature and pressure? M_O =16,M_N =14