A sealed bottle contains air at 22 ° C and a pressure 12 . 0 × 10 5 Pa . The temperature is raised to 120 . 0 ° C . Calculate the new pressure.

Given, Temperature, T 1 = 22 ° C = 22 + 273 . 15 = 295 . 15 K , Pressure, P 1 = 12 . 0 × 10 5 Pa T 2 = 120 . 0 ° C = 120 + 273 . 15 = 393 . 15 K , P 2 = ? From Gay- Lussac's law, the pressure is directly proportional to the temperature at the constant volume. P 2 P 1 = T 2 T 1 P 2 = P 1 T 2 T 1 P 2 = 12 . 0 × 10 5 × 393 . 15 295 . 15 = 15 . 98 × 10 5 Pa Hence, the new pressure is 15 . 98 × 10 5 Pa .

A gas has pressure 8 . 2 × 10 6 Pa and volume 2 . 3 × 10 - 3 m 3 . The pressure is reduced to 4 . 5 × 10 6 Pa at constant temperature. Calculate the new volume of the gas.

Given, P 1 = 8 . 2 × 10 6 Pa , V 1 = 2 . 3 × 10 - 3 m 3 P 2 = 4 . 5 × 10 6 Pa , V 2 = ? The pressure is inversely proportional to the volume at the constant temperature. V 2 V 1 = P 1 P 2 V 2 = P 1 P 2 V 1 V 2 = 8 . 2 × 10 6 4 . 5 × 10 6 × 2 . 3 × 10 - 3 V 2 = 4 . 1911 × 10 - 3 m - 3 Hence, the new volume of the gas is 4 . 1911 × 10 - 3 m - 3 .

A mass of 12 . 0 kg of helium is required to fill a bottle with volume 5 . 00 × 10 - 3 m 3 at a temperature of 20 . 0 ° C . Determine the pressure in helium.

Given, The given mass of Helium, m = 12 . 0 × 10 3 g The volume required to fill a bottle, V = 5 . 00 × 10 - 3 m 3 Temperature, T = 20 ° C = 20 + 273 . 15 = 293 . 15 K The molecular mass of the Helium, M = 4 g / mol We know that, n = m M n = 12 . 0 × 10 3 4 = 3000 mol From the ideal gas equation, P V = n R T P = n R T V P = 3000 × 8 . 31 × 293 . 15 5 . 00 × 10 - 3 P = 1 . 461 × 10 9 Pa Hence, the pressure in helium is 1 . 461 × 10 9 Pa .

Determine the mass of carbon dioxide required to fill a tank with volume 12 . 0 × 10 - 3 m 3 at a temperature of 20 . 0 ° C and a pressure of 4 . 00 atm .

Given, The molecular mass of carbon dioxide, M = 44 g / mol The volume required to fill a tank, V = 12 . 0 × 10 - 3 m 3 Temperature, T = 20 . 0 ° C = 20 . 0 + 273 = 293 K Pressure, P = 4 . 00 atm = 4 × 1 . 013 × 10 5 = 4 . 052 × 10 5 Pa From the ideal gas equation, P V = m M R T P V M = m R T m = P V M R T m = 4 . 052 × 10 5 × 12 . 0 × 10 - 3 × 44 8 . 31 × 293 m = 87 . 86 g Hence, the mass of the carbon dioxide is 87 . 86 g .

E M B I B E

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 13

MEDIUM

Diploma

IMPORTANT

Earn 100

Calculate the number of molecules in $28 g$ of hydrogen gas (molar mass $2 g {mol}^{- 1}$ ).

Important Questions on Thermal Physics

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 14

Calculate the number of moles in

6.0 g

of helium gas (molar mass

4 g {mol}^{- 1}

).

EASY

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 15

Determine the number of moles in a sample of a gas that contains

2.0 \times 10^{24}

molecules.

MEDIUM

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 16

Determine the mass in grams of carbon (molar mass

12 g {mol}^{- 1}

) that contain as many molecules as

21 g

of krypton (molar mass

84 g {mol}^{- 1}

).

MEDIUM

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 17

A sealed bottle contains air at

22 ° C

and a pressure

12.0 \times 10^{5} Pa

. The temperature is raised to

120.0 ° C

. Calculate the new pressure.

MEDIUM

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 18

A gas has pressure

8.2 \times 10^{6} Pa

and volume

2.3 \times 10^{- 3} m^{3}

. The pressure is reduced to

4.5 \times 10^{6} Pa

at constant temperature. Calculate the new volume of the gas.

MEDIUM

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 19

A mass of

12.0 kg

of helium is required to fill a bottle with volume

5.00 \times 10^{- 3} m^{3}

at a temperature of

20.0 ° C

. Determine the pressure in helium.

MEDIUM

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 20

Determine the mass of carbon dioxide required to fill a tank with volume

12.0 \times 10^{- 3} m^{3}

at a temperature of

20.0 ° C

and a pressure of

4.00 atm

.

HARD

Diploma

IMPORTANT

Physics for the IB Diploma 6th Edition>Chapter 3 - Thermal Physics>Test yourself>Q 21

A flask of the volume

300.0 \times 10^{- 6} m^{3}

contains air at pressure of

5.00 \times 10^{5} Pa

and a temperature

27.0 ° C

. The flask loses molecules at a rate

3.00 \times 10^{19}

per second. Estimate how long it takes for the pressure in the flask to fall to half its original value.( Assume that the temperature of the air remains constant during this time.)