A sealed cubical container $20\mathrm{.}0$ cm on a side contains a gas with two times Avogadro's number of neon atoms at a temperature of $18\mathrm{.}0$C$.$

HINT

$($a$)$

Find the internal energy $($in J$)$ of the gas.

J

$($b$)$

The total translational kinetic energy $($in J$)$ of the gas.

J

$($c$)$

Calculate the average kinetic energy $($in J$)$ per atom.

J

$($d$)$

Use

P $=$

$23$

NV

$12$

mv$2$

to calculate the gas pressure $($in Pa$).$

Pa

$($e$)$

Calculate the gas pressure $($in Pa$)$ using the ideal gas law

$($PV $=$ nRT$).$

The gas pressure can be calculated using either

P $=$

$23$

NV

$12$

mv$2$

or the ideal gas law. To within rounding error, each expression gives the correct answer. The algebra below shows that the two expressions are equal.

P $=$

$23$

NV

$12$

mv$2$

$=$

$23$

nNAV

$32$

RTNA

$=$

nRTV