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

Answer:

(a). The change in the average kinetic energy per atom is $1.57\times10^{-21}\ eV$.

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

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

$\Delta K.E=\dfrac{3}{2}k\Delta t$

Put the value into the formula

$\Delta K.E=\dfrac{3}{2}\times1.38\times10^{-23}\times(362-286)$

$\Delta K.E=1.57\times10^{-21}\ eV$

(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

$\Delta U=mg\Delta h$

$\Delta h =\dfrac{\Delta U}{mg}$

$\Delta h=\dfrac{1.57\times10^{-21}}{40.0\times1.66\times10^{-27}\times9.8}$

$\Delta h=2412.7=2413\ m$

Hence, (a). The change in the average kinetic energy per atom is $1.57\times10^{-21}\ eV$.

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