Determine the work done during the adiabatic expansion of 10 moles of an ideal monatomic

Determine the work done during the adiabatic expansion of 10 moles of an ideal monatomic gas if its temperature has decreased by 30 K.

We start by recording given:

v (nu) = 10 mol;

adiabatic process;

ΔT = 30 ° K.

Find:

A ‘-?

To find a job, apply the formula:

-A ‘= + Δ U;

Δ U = 3m / 2M * R * ΔT;

v (nu) = m / M;

Substituting into the formula above and we get:

Δ U = 3v / 2 * R * ΔT.

And we get the formula for calculating the work:

-A ‘= + 3v / 2 * R * ΔT.

A ‘= – 3v / 2 * R * ΔT.

It remains for us to substitute the values into the formula and perform calculations:

A ‘= – (3 * 10 mol * 8.32 J / ° K * 30 ° K) / 2 = -3 739.5 J.

The work done during the adiabatic expansion of 10 moles of an ideal monatomic gas with a decrease in temperature by 30 K is equal to -3,739.5 J.