Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law

Problem 43

Chapter 17, Problem 43

A sealed metal container contains a gas at 30.0°C and absolute pressure 1.00 atm. To what temperature must the gas be heated for the pressure to double to 2.00 atm? (Ignore expansion of the container.)

Verified step by step guidance

Start by identifying the relationship between pressure and temperature for a gas in a sealed container. Since the volume and the amount of gas remain constant, we can use the Gay-Lussac's Law:

\frac{P}{T} = \frac{P_{1}}{T_{1}}

, where P is pressure and T is temperature in Kelvin.

Rearrange the formula to solve for the final temperature

T_{2}

T_{2} = \frac{P_{2}}{T_{1}} / P_{1}

Convert the initial temperature from Celsius to Kelvin, since the gas law requires temperatures in Kelvin. Use the formula:

T

₁ = T_C + 273.15. For

T

_C = 30.0, calculate

T

₁.

Substitute the known values into the rearranged formula:

T_{2} = \frac{P_{2}}{T_{1}} / P_{1}

, where

P_{1} = 1.00

atm,

P_{2} = 2.00

atm, and

T_{1}

is the temperature in Kelvin from the previous step.

After calculating

T_{2}

in Kelvin, if needed, convert it back to Celsius using the formula:

T

_C = T_K - 273.15. This will give the final temperature in Celsius.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. In this context, it helps us understand how changes in temperature affect pressure when the volume and amount of gas remain constant.

Absolute Temperature

Absolute temperature is measured in Kelvin and is crucial for gas law calculations. It is obtained by adding 273.15 to the Celsius temperature. Since gas laws require temperature in absolute terms, converting Celsius to Kelvin is essential for accurate results.

Charles's Law

Charles's Law states that the volume of a gas is directly proportional to its absolute temperature when pressure is held constant. Although this problem involves pressure changes, understanding this law helps in grasping the relationship between temperature and pressure in gas behavior.

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A helium-filled balloon escapes a child’s hand at sea level and 20.0°C. When it reaches an altitude of 3600 m, where the temperature is 5.0°C and the pressure only 0.64 atm, how will its volume compare to that at sea level?

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What is the pressure inside a 41.0-L container holding 105.0 kg of argon gas at 21.6°C?

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