Ch 20: The Micro/Macro Connection

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 20: The Micro/Macro Connection

문제 18

20장, 문제 18

The rms speed of molecules in a gas is 600 m/s. What will be the rms speed if the gas pressure and volume are both halved?

검증된 단계별 안내

The root mean square (rms) speed of gas molecules is given by the formula:

\sqrt{\frac{3 k T}{m}}

, where

k

is the Boltzmann constant,

T

is the temperature, and

m

is the mass of a single molecule.

The rms speed depends on the temperature

T

, so we need to determine how the temperature changes when the pressure and volume are halved.

Using the ideal gas law,

P V = n R T

, where

P

is pressure,

V

is volume,

n

is the number of moles, and

R

is the gas constant, we can express the temperature as

T = \frac{P V}{n R}

. If both

P

and

V

are halved, their product remains constant, so

T

does not change.

Since the temperature

T

remains constant, the rms speed of the gas molecules also remains unchanged. This is because the rms speed is directly proportional to the square root of the temperature, as shown in the formula in Step 1.

Thus, the rms speed of the gas molecules will still be 600 m/s, even after the pressure and volume are halved.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Root Mean Square (RMS) Speed

The root mean square speed is a measure of the average speed of particles in a gas, calculated as the square root of the average of the squares of the speeds of the individual particles. It is a crucial concept in kinetic theory, reflecting the energy and temperature of the gas. The RMS speed is directly related to the temperature and molecular mass of the gas.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of an ideal 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. This law helps in understanding how changes in pressure and volume affect the behavior of gases.

Kinetic Theory of Gases

The Kinetic Theory of Gases explains the behavior of gases in terms of the motion of their molecules. It posits that gas pressure results from collisions of molecules with the walls of a container and that temperature is a measure of the average kinetic energy of the molecules. This theory provides insights into how changes in pressure and volume influence the speed and energy of gas molecules.