Skip to main content
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: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 17 - Temperature, Thermal Expansion, and the Ideal Gas LawProblema 45
Capitolo 17, Problema 45

If 59.2 L of oxygen at 18.0°C and an absolute pressure of 2.45 atm are compressed to 38.8 L and at the same time the temperature is raised to 56.0°C, what will the new pressure be?

Guida verificata passo dopo passo
1
Start by identifying the given values: initial volume \( V_1 = 59.2 \; \text{L} \), initial temperature \( T_1 = 18.0^\circ \text{C} = 291.15 \; \text{K} \) (convert to Kelvin by adding 273.15), initial pressure \( P_1 = 2.45 \; \text{atm} \), final volume \( V_2 = 38.8 \; \text{L} \), and final temperature \( T_2 = 56.0^\circ \text{C} = 329.15 \; \text{K} \). The goal is to find the final pressure \( P_2 \).
Use the combined gas law, which relates pressure, volume, and temperature: \( \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \). Rearrange this equation to solve for \( P_2 \): \( P_2 = P_1 \cdot \frac{V_1}{V_2} \cdot \frac{T_2}{T_1} \).
Substitute the known values into the equation: \( P_2 = 2.45 \; \text{atm} \cdot \frac{59.2 \; \text{L}}{38.8 \; \text{L}} \cdot \frac{329.15 \; \text{K}}{291.15 \; \text{K}} \).
Simplify the fractions for volume and temperature: \( \frac{59.2}{38.8} \) and \( \frac{329.15}{291.15} \). Then multiply these ratios with the initial pressure \( P_1 \).
The result of the calculation will give you the final pressure \( P_2 \) in atm. Ensure that the units are consistent throughout the calculation to maintain accuracy.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
5m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to predict how a gas will behave under changing conditions.
Video consigliato:
Percorso guidato
07:21
Ideal Gases and the Ideal Gas Law

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. Mathematically, it can be expressed as V1/T1 = V2/T2. This principle is crucial for understanding how temperature changes affect the volume of a gas, which is relevant in the given problem.
Video consigliato:
Percorso guidato
10:20
Gauss' Law

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature is held constant. This relationship can be expressed as P1V1 = P2V2. In the context of the problem, this law helps to understand how the pressure of the gas will change as its volume is altered, especially when combined with temperature changes.
Video consigliato:
Percorso guidato
10:20
Gauss' Law
Pratica correlata
Domanda del libro di testo

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?

845
views
Domanda del libro di testo

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

1562
views
Domanda del libro di testo

A helium balloon rises because of a buoyant force. By what percentage does the buoyant force on a helium balloon change if the temperature of the helium is increased from 15°C to 25°C while the temperature of the surrounding air is unchanged? Assume that the pressure of the helium remains constant.

975
views
Domanda del libro di testo

You buy an “airtight” potato chip bag packaged at sea level, and take the chips on an airplane flight. When you take the potato chip bag out of your “carry-on” bag, you notice it has noticeably “puffed up.” Airplane cabins are typically pressurized at 0.75 atm, and assuming the temperature inside an airplane is about the same as inside a potato chip processing plant, by what percentage has the bag “puffed up” in comparison to when it was packaged?

908
views
Domanda del libro di testo

A storage tank at STP contains 26.5 kg of nitrogen (N₂). What is the volume of the tank?

76
views
Domanda del libro di testo

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.)

944
views