You have a sample of helium gas at -33^∘ C, and you want to increase the average speed of helium

You have a sample of helium gas at -33^∘ C, and you want to...

Key Concepts

Scaling of Speed with Temperature

When the average speed of gas particles is increased by a given percentage, this change relates to the temperature by the square of that percentage change. For instance, to achieve a 10% increase in average speed, the temperature must be scaled by the square of 1.10 (i.e., multiplied by approximately 1.21). This scaling law is a direct consequence of the square-root dependence between speed and temperature.

Relationship between Molecular Speed and Temperature

The average speed of gas particles is directly related to the temperature by a square-root dependence; specifically, the speed is proportional to the square root of the temperature (v ? ?T). This principle is key to understanding how changes in temperature affect the motion of gas molecules.

Absolute Temperature Scale

In thermodynamics, temperatures in equations of molecular motion must be expressed in an absolute scale, typically Kelvin, since many physical relationships (such as those in the kinetic theory of gases) involve temperature measured from absolute zero. Converting Celsius to Kelvin is essential when applying these equations.

Kinetic Theory of Gases

The kinetic theory of gases describes the motion of particles in a gas and relates the average kinetic energy of the particles to the temperature of the gas. For a monatomic gas, the average kinetic energy is proportional to the absolute temperature, making it a fundamental concept in understanding how temperature influences molecular speeds.

Transcript

00:01 In this question, we have a sample of helium gas that is at a temperature of negative 33 degrees celsius.

00:17 And we want to increase the average speed of the helium atoms by 10%.

00:27 Okay? so you want speed 2 to be 10 %? higher than speed one.

00:36 So it would be speed one plus 10 % of speed one, which means 1 .1 speed 1.

00:52 This is what you want to achieve.

00:55 The relationship that relates average speed of atoms or molecules, for that matter, of gases to temperature is a maxwell equation.

01:11 The but the equation say that the velocity or the average speed of gas particles equals the square root of three, the constant of the ideal gas, times the temperature divided by the molar mass of the gas.

01:40 Okay? now, there are a couple of things that you need to remember when using this equation.

01:45 This equation is completely based on a si unit, a system international or international system of units.

01:57 Therefore, the concept of the ideal gas must be used as 8 .314 yules per mole per kelvin.

02:16 Okay? the temperature is in kelvin's.

02:20 You know that even from the constant of the ideal gas.

02:26 And the molar mass, because we are all working here with si units, must be kilograms per mole, as opposed as grams per mole.

02:43 And then the velocity will be meters per second.

02:52 That's how you're going to get the velocity...

Please give Ace some feedback