Question

A gas cylinder contains argon atoms (m=40.0 u). The temperature is increased from 286 K (13°C) to 362 K (89°C) (a) What is the change in the average kinetic energy per atom? eV (b) The container is resting on a table in the Earth's gravity. Find the change in the vertical position of the container that produces the same change in the average energy per atom found in part

Answer 1

(a). The change in the average kinetic energy per atom is
`1.57*10^(-21)\ eV`.

(b). The change in vertical position is 2413 m.

Step-by-step explanation:

Given that,

Mass = 40.0 u

The increased temperature from 286 K to 362 K.

(a). We need to calculate the change in the average kinetic energy per atom

Using formula of kinetic energy

`\Delta K.E=(3)/(2)k\Delta t`

Put the value into the formula

`\Delta K.E=(3)/(2)*1.38*10^(-23)*(362-286)`

`\Delta K.E=1.57*10^(-21)\ eV`

(b). The change in potential energy of the container due to change in the vertical position

We need to calculate the change in vertical position

Using formula of potential energy

`\Delta U=mg\Delta h`

`\Delta h =(\Delta U)/(mg)`

`\Delta h=(1.57*10^(-21))/(40.0*1.66*10^(-27)*9.8)`

`\Delta h=2412.7=2413\ m`

Hence, (a). The change in the average kinetic energy per atom is
`1.57*10^(-21)\ eV`.

(b). The change in vertical position is 2413 m.