Answer to Question #283149 in Physics for Kimgcash

Question

Neon is a monatomic gas, in which inter-molecular forces are extremely weak. 1.00 kg

of neon gas has a density of 0.828 kgm-3 at 100 kPa and 293 K. Find the :

(a) average kinetic energy of each gas molecule

(b) total kinetic energy of the gas.

(c) Root-mean-square speed (crms)

If the neon gas is compressed to double its density, while keeping the temperature the

same:

(d) What are the values for (a)-(c) at the new pressure and volume?

Answer 1

a)

$$KE_m=\dfrac12 mv_\text{rms}^2=6.08·10^{-21}\text{ J}.$$

b)

$$KE=\dfrac32 k_bNT=3.03·10^{-19}\text{ J}.$$

c)

$$v_\text{rms}=\sqrt\dfrac{3RT}{M}=605\text{ m/s}.$$

d)

$$KE_m=\dfrac12 mv_\text{rms}^2=6.08·10^{-21}\text{ J}.\\\space\\ KE_g=\dfrac32 k_bNT=3.03·10^{-19}\text{ J}.\\\space\\ v_\text{rms}=\sqrt\dfrac{3RT}{M}=605\text{ m/s}.$$