Which of the following statements are true? check all that apply.-the average speed of gas molecules is independent of temperature.-there are gas molecules that move slower than the average.-the average speed of gas molecules increases with increasing temperature.-the average kinetic energy of gas molecules decreases with decreasing temperature.-the temperature of a gas sample is related to the average kinetic energy.

The average speed of gas molecules is independent of temperature. (False)

There are gas molecules that move slower than the average (True)

The average speed of gas molecules increases with increasing temperature. (True)

The average kinetic energy of gas molecules decreases with decreasing temperature. (True)

The temperature of a gas sample is related to the average kinetic energy. (True)

Explanation:

The average speed of gas molecules is independent of temperature. (False)

The equation for the average speed of gas molecules is giving as:

  (1)

Where is the Boltzmann's Constant, m is the mass of a gas molecule and T is the temperature.

The expression for the average speed of gas molecules is get by using the kinetic theory and the ideal gas law. Equation 1 shows that the average velocity is directly proportional to the temperature, So when the temperature increase, the average velocity will increase too. That leaves clear than the average velocity is always dependent of the temperature.    

There are gas molecules that move slower than the average (True)

Gas molecules are in constant movement with aleatory directions. That leads to different collision between particles and the walls of the container, Some of the particles will move faster and other slower as a consequence of the different collisions.

So it is correct to say that there are gas molecules that move slower than the average.  

The average speed of gas molecules increases with increasing temperature. (True)

As it was already demonstrated in equation 1.

The average kinetic energy of gas molecules decreases with decreasing temperature. (True)

The equation for the average kinetic energy is giving as:

 (2)

Which indicates that the average kinetic energy is directly proportional to the temperature. That means that as the kinetic energy increase the temperature of the whole gas will do it too. So the kinetic energy will decrease with decreasing temperature.

The temperature of a gas sample is related to the average kinetic energy. (True)

It can be understood with the same approach from the explanation above, just rewriting equation 2 for the temperature (T):

  (3)

.) the observation by semmelweis that more mothers died of childbed fever when their doctors also worked in the morgue

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .