Question 1

A spherical air bubble originating from a scuba diver at a depth of 15 m has a diameter of 0.8 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )

Accepted Answer

This question can be solved using Boyle's Law, which states that the volume of a gas is inversely proportional to the pressure it experiences. As the air bubble rises to the surface, the pressure exerted on it decreases while the volume of the bubble increases.

The pressure at the surface is approximately 1 atm or 101.3 kPa. At a depth of 15 m, the pressure is about 2.5 atm or 253.8 kPa.

Using the formula:

P1V1 = P2V2

where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

We can rearrange the formula to solve for V2:

V2 = (P1/P2) x V1

Plugging in the values:

V2 = (253.8 kPa / 101.3 kPa) x (4/3 x pi x (0.4 cm)^3)

V2 = 1.1 cm

Therefore, the bubble's diameter when it reaches the surface will be approximately 1.1 cm, which is answer choice C.

Question 2

An ideal gas is confined to a container with constant volume.The number of moles is constant.By what factor will the pressure change if the absolute temperature triples?

Accepted Answer

According to the ideal gas law, PV = nRT, if the volume (V) and the number of moles (n) are constant, then P/T = constant or P1/T1 = P2/T2. Therefore, if the temperature (T) triples (i.e., T2 = 3T1), the pressure (P) will also triple (i.e., P2 = 3P1). Thus, the factor by which the pressure changes is (P2/P1) = 3.0. Therefore, the best choice is C) 3.0.

Question 3

The mass of a hot-air balloon and its cargo (not including the air inside)is 150 kg.The air outside is at a temperature of 10°C and a pressure of 1 atm = 10⁵ N/m².The volume of the balloon is 600 m³.Which temperature below of the air in the balloon will allow the balloon to just lift off? (Air density at 10°C is 1.25 kg/m³. )

Accepted Answer

To lift off, the buoyant force must equal the weight of the balloon and its cargo. The buoyant force is the weight of the displaced air, which depends on the density difference between the inside and outside air. Using the ideal gas law and the given conditions, the temperature inside the balloon must be 71°C for the balloon to lift off.

Question 4

One way to heat a gas is to compress it.A gas at 2 atm at 31°C is compressed to two fifths of its original volume,and it reaches 36 atm pressure.What is its new temperature?

Accepted Answer

The answer of One way to heat a gas is...

Question 5

With molar quantity and temperature held constant,by what factor does the pressure of an ideal gas change when the volume is five times bigger?

Accepted Answer

According to Boyle's Law, for a given amount of gas at constant temperature, the pressure is inversely proportional to the volume. If the volume increases by a factor of 5, the pressure decreases by a factor of 1/5, which is 0.2.

Question 6

Two moles of an ideal gas at 4 atm and 15°C are heated up to 170 °C.If the volume is held constant during this heating,what is the final pressure?

Accepted Answer

Using the ideal gas law and the relation P1/T1 = P2/T2 (where T is in Kelvin), we convert temperatures to Kelvin (15°C = 288K and 170°C = 443K) and solve for P2: P2 = P1 * (T2/T1) = 4 atm * (443/288) = 6.2 atm.

Question 7

9.0 g of water in a 2.0-L pressure vessel is heated to 500°C.What is the pressure inside the container? (R = 0.082 L⋅atm/mol⋅K,one mole of water has a mass of 18 grams)

Accepted Answer

The answer of 9.0 g of water in a 2.0-L...

Question 8

An ideal gas is confined to a container with adjustable volume.The number of moles and temperature are constant.By what factor will the volume change if pressure triples?

Accepted Answer

According to Boyle's law, at constant temperature and number of moles, the pressure of an ideal gas is inversely proportional to its volume. Therefore, if the pressure triples, the volume must decrease by a factor of 3, which means the new volume will be one-third of the initial volume. Hence, the correct choice is B, i.e. 1/3.

Question 9

Tricia puts 47 g of dry ice (solid CO₂)into a 4-L container and seals the top.The dry ice turns to gas at room temperature (20°C).Find the pressure increase in the 4-L container.(One mole of CO₂ has a mass of 47 g,R = 0.082 1 L⋅atm/mol⋅K.Ignore the initial volume of the dry ice. )

Accepted Answer

To solve this problem, we can use the ideal gas law: PV = nRT We don't know the final volume or the number of moles of gas, but we do know the initial number of moles of dry ice. We can use the fact that dry ice (CO₂) sublimes into one mole of gas: CO₂(s) → CO₂(g) So, we have one mole of gas in a 4 L container at 20°C. We can plug in the values we know: P(4 L) = (1 mol)(0.0821 L⋅atm/mol⋅K)(293 K) Solving for P, we get: P = 6 atm Therefore, the pressure increase in the 4-L container is 6 atm. The answer is B.

Question 10

How many atoms are present in a sample of pure iron with a mass of 260 g? (The atomic mass of iron = 56 and N_A = 6.02 × 10²³)

Accepted Answer

The answer of How many atoms are present in a...

Question 11

A helium-filled weather balloon has a 1.2 m radius at liftoff where air pressure is 2 atm and the temperature is 278 K.When airborne,the temperature is 227 K,and its radius expands to 2 m.What is the pressure at the airborne location?

Accepted Answer

The combined gas law can be used to solve this problem:

(P1V1/T1) = (P2V2/T2)

First, we need to convert the radius to volume using the formula for the volume of a sphere:

V1 = (4/3)π(1.2 m)^3 = 7.239 m^3     (at liftoff)
V2 = (4/3)π(2 m)^3 = 33.51 m^3       (airborne)

Next, we can plug in the given values:

(P1V1/T1) = (P2V2/T2)
(2 atm)(7.239 m^3)/(278 K) = P2(33.51 m^3)/(227 K)

Simplifying gives:

P2 = (2 atm)(7.239 m^3)(227 K)/(33.51 m^3)(278 K) = 0.353 atm

Therefore, the answer is C.

Question 12

A pressure of 3 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 286 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and N_A = 6.02 × 10²³)

Accepted Answer

The answer of A pressure of 3 × 10−⁷ mm...

Question 13

A 3-L container holds half a mole of an ideal gas at a pressure of 12 atm.What is the gas temperature? (R = 0.082 1 L⋅atm/mol⋅K)

Accepted Answer

We can use the ideal gas law in the form:

PV = nRT

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

Rearranging this equation, we get:

T = PV/nR

Plugging in the given values, we get:

T = (12 atm) x (3 L) / (0.5 mol) x (0.0821 L.atm/mol.K)

T = 878 K

Therefore, the answer is choice D) 878 K.

Question 14

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 333 K,and the pressure is 1.14 × 10⁶ N/m²,what is the volume? (R = 8.31 J/mol⋅K)

Accepted Answer

Using the ideal gas law PV = nRT, where P = 1.14 × 10^6 N/m^2, n = 2 moles, R = 8.31 J/mol⋅K, and T = 333 K, the volume V can be calculated as V = nRT/P = (2 * 8.31 * 333) / (1.14 × 10^6) = 4.85 × 10^-3 m^3.

Question 15

Boltzmann's constant,k_B,may be derived as a function of R,the universal gas constant,and N_A,Avogadro's number.Which expresses the value of k_B?

Accepted Answer

Boltzmann's constant (k) is defined as the universal gas constant (R) divided by Avogadro's number (N_A), thus k = R/N_A.

Question 16

With volume and molar quantity held constant,by what factor does the absolute temperature change for an ideal gas when the pressure is five times bigger?

Accepted Answer

According to the ideal gas law (PV = nRT), if volume (V) and molar quantity (n) are constant, the pressure (P) is directly proportional to the absolute temperature (T). Therefore, if the pressure is increased by a factor of 5, the temperature must also increase by a factor of 5 to maintain the equality.

Question 17

One mole of an ideal gas at 1.00 atm and 0.00°C occupies 22.4 L.How many molecules of an ideal gas are in four cm³ under these conditions?

Accepted Answer

The answer of One mole of an ideal gas at...

Question 18

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the molecular mass of nitrogen is 28,how many grams of nitrogen are present?

Accepted Answer

One mole of any gas at standard pressure and temperature (STP) occupies 22.4 liters. As there are two moles of nitrogen in the cylinder, the volume of nitrogen gas will be 2 x 22.4 liters = 44.8 L. To calculate the mass of nitrogen, we use the formula:

mass = number of moles x molecular mass

Therefore, mass of nitrogen = 2 moles x 28 g/mol = 56 grams. 
Therefore, the correct answer is choice B.

Question 19

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 250 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

Accepted Answer

The answer of Estimate the volume of a helium-filled balloon...

Question 20

How many moles of air must escape from a 12-m × 10-m × 3-m room when the temperature is raised from 5°C to 25°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

Accepted Answer

We can use the ideal gas law, PV=nRT, to solve for the number of moles of air that must escape. Since the pressure remains unchanged, we can simplify the equation to V/n=RT/P. We can calculate the initial volume of the room as V=12m x 10m x 3m = 360 m^3. Given the temperature change from 5°C to 25°C, the change in temperature is ΔT = 20°C = 20 K. R is the gas constant, which is 8.31 J/mol K. Therefore, we have:

V/n = (8.31 J/mol K)(298 K)/ (1 atm x 101,325 Pa/atm x 360 m^3)
n = V(1 atm x 101,325 Pa/atm)/(8.31 J/mol K)(298 K) = 1.1 x 10^13 mol

Therefore, approximately 1.1 x 10^13 moles of air must escape from the room. The closest answer choice is B.

Quiz 10: Thermal Physics

A spherical air bubble originating from a scuba diver at a depth of 15 m has a diameter of 0.8 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )

An ideal gas is confined to a container with constant volume.The number of moles is constant.By what factor will the pressure change if the absolute temperature triples?

One way to heat a gas is to compress it.A gas at 2 atm at 31°C is compressed to two fifths of its original volume,and it reaches 36 atm pressure.What is its new temperature?

With molar quantity and temperature held constant,by what factor does the pressure of an ideal gas change when the volume is five times bigger?

Two moles of an ideal gas at 4 atm and 15°C are heated up to 170 °C.If the volume is held constant during this heating,what is the final pressure?

9.0 g of water in a 2.0-L pressure vessel is heated to 500°C.What is the pressure inside the container? (R = 0.082 L⋅atm/mol⋅K,one mole of water has a mass of 18 grams)

An ideal gas is confined to a container with adjustable volume.The number of moles and temperature are constant.By what factor will the volume change if pressure triples?

Tricia puts 47 g of dry ice (solid CO₂) into a 4-L container and seals the top.The dry ice turns to gas at room temperature (20°C) .Find the pressure increase in the 4-L container.(One mole of CO₂ has a mass of 47 g,R = 0.082 1 L⋅atm/mol⋅K.Ignore the initial volume of the dry ice. )

How many atoms are present in a sample of pure iron with a mass of 260 g? (The atomic mass of iron = 56 and N_A = 6.02 × 10²³)

A helium-filled weather balloon has a 1.2 m radius at liftoff where air pressure is 2 atm and the temperature is 278 K.When airborne,the temperature is 227 K,and its radius expands to 2 m.What is the pressure at the airborne location?

A pressure of 3 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 286 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and N_A = 6.02 × 10²³)

A 3-L container holds half a mole of an ideal gas at a pressure of 12 atm.What is the gas temperature? (R = 0.082 1 L⋅atm/mol⋅K)

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 333 K,and the pressure is 1.14 × 10⁶ N/m²,what is the volume? (R = 8.31 J/mol⋅K)

Boltzmann's constant,k_B,may be derived as a function of R,the universal gas constant,and N_A,Avogadro's number.Which expresses the value of k_B?

With volume and molar quantity held constant,by what factor does the absolute temperature change for an ideal gas when the pressure is five times bigger?

One mole of an ideal gas at 1.00 atm and 0.00°C occupies 22.4 L.How many molecules of an ideal gas are in four cm³ under these conditions?

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the molecular mass of nitrogen is 28,how many grams of nitrogen are present?

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 250 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.

How many moles of air must escape from a 12-m × 10-m × 3-m room when the temperature is raised from 5°C to 25°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

Quiz 10: Thermal Physics

A spherical air bubble originating from a scuba diver at a depth of 15 m has a diameter of 0.8 cm.What will the bubble's diameter be when it reaches the surface? (Assume constant temperature. )

An ideal gas is confined to a container with constant volume.The number of moles is constant.By what factor will the pressure change if the absolute temperature triples?

One way to heat a gas is to compress it.A gas at 2 atm at 31°C is compressed to two fifths of its original volume,and it reaches 36 atm pressure.What is its new temperature?

With molar quantity and temperature held constant,by what factor does the pressure of an ideal gas change when the volume is five times bigger?

Two moles of an ideal gas at 4 atm and 15°C are heated up to 170 °C.If the volume is held constant during this heating,what is the final pressure?

9.0 g of water in a 2.0-L pressure vessel is heated to 500°C.What is the pressure inside the container? (R = 0.082 L⋅atm/mol⋅K,one mole of water has a mass of 18 grams)

An ideal gas is confined to a container with adjustable volume.The number of moles and temperature are constant.By what factor will the volume change if pressure triples?

Tricia puts 47 g of dry ice (solid CO2) into a 4-L container and seals the top.The dry ice turns to gas at room temperature (20°C) .Find the pressure increase in the 4-L container.(One mole of CO2 has a mass of 47 g,R = 0.082 1 L⋅atm/mol⋅K.Ignore the initial volume of the dry ice. )

How many atoms are present in a sample of pure iron with a mass of 260 g? (The atomic mass of iron = 56 and NA = 6.02 × 1023)

A helium-filled weather balloon has a 1.2 m radius at liftoff where air pressure is 2 atm and the temperature is 278 K.When airborne,the temperature is 227 K,and its radius expands to 2 m.What is the pressure at the airborne location?

A pressure of 3 × 10−7 mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 286 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and NA = 6.02 × 1023)

A 3-L container holds half a mole of an ideal gas at a pressure of 12 atm.What is the gas temperature? (R = 0.082 1 L⋅atm/mol⋅K)

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 333 K,and the pressure is 1.14 × 106 N/m2,what is the volume? (R = 8.31 J/mol⋅K)

Boltzmann's constant,kB,may be derived as a function of R,the universal gas constant,and NA,Avogadro's number.Which expresses the value of kB?

With volume and molar quantity held constant,by what factor does the absolute temperature change for an ideal gas when the pressure is five times bigger?

One mole of an ideal gas at 1.00 atm and 0.00°C occupies 22.4 L.How many molecules of an ideal gas are in four cm3 under these conditions?

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the molecular mass of nitrogen is 28,how many grams of nitrogen are present?

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 250 kg.The density of air is 1.29 kg/m3 and helium has a density of 0.178 kg/m3.

How many moles of air must escape from a 12-m × 10-m × 3-m room when the temperature is raised from 5°C to 25°C? Assume the pressure remains unchanged at one atmosphere while the room is heated.

Tricia puts 47 g of dry ice (solid CO₂) into a 4-L container and seals the top.The dry ice turns to gas at room temperature (20°C) .Find the pressure increase in the 4-L container.(One mole of CO₂ has a mass of 47 g,R = 0.082 1 L⋅atm/mol⋅K.Ignore the initial volume of the dry ice. )

How many atoms are present in a sample of pure iron with a mass of 260 g? (The atomic mass of iron = 56 and N_A = 6.02 × 10²³)

A pressure of 3 × 10−⁷ mm of Hg is achieved in a vacuum system.How many gas molecules are present per liter volume if the temperature is 286 K? (760 mm of Hg = 1 atm,R = 0.082 1 L⋅atm/mol⋅K,and N_A = 6.02 × 10²³)

Two moles of nitrogen gas are contained in an enclosed cylinder with a movable piston.If the gas temperature is 333 K,and the pressure is 1.14 × 10⁶ N/m²,what is the volume? (R = 8.31 J/mol⋅K)

Boltzmann's constant,k_B,may be derived as a function of R,the universal gas constant,and N_A,Avogadro's number.Which expresses the value of k_B?

One mole of an ideal gas at 1.00 atm and 0.00°C occupies 22.4 L.How many molecules of an ideal gas are in four cm³ under these conditions?

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 250 kg.The density of air is 1.29 kg/m³ and helium has a density of 0.178 kg/m³.