A cylinder with a piston contains 0.180 m o l of nitrogen at 1.60×10 5 P a and 3

Question

A cylinder with a piston contains 0.180 mol of nitrogen at 1.60×105 Pa and 310 K . The nitrogen may be treated as an ideal gas. The gas is first compressed isobarically to half its original volume. It then expands adiabatically back to its original volume, and finally it is heated isochorically to its original pressure.

Find the internal-energy change of the gas during the adiabatic expansion.

Find the heat added to the gas during the final heating.

Find the internal-energy change of the gas during the final heating.

Explanation / Answer

With the initial data we can calculate the initial volume using ideal gas ecuation

V1=n*R*T/P = 0.180*8.314*310/(1.60*10^5) = 2,899*10^-3 m3

then we know

deltaE=q-w where deltaE is internal-energy change, q is heat transfered and w is work,

now, the expasion is adiabatic(q=0), so deltaE = -w

where w=P(v2-v1) but we know v2 is 2*v1 as the problem says, so w=P*v1 = (1.60*10^5)Pa * 2,899*10^-3 m3

w= 463.9 J

so deltaE=-463.9 J dinring the adiabatic expasion

Finally, q.ad=deltaE (where q.ad is the heat added) and thsi is because in a isochorical process work=0

so, i will calculate the heat added

q=n*Cp*deltaT,

Now, by the Gay-Lussac law we now if preasure is divide to a half, so do the temperature for ideal gas, so

deltaT = 310K-155K=155K

so, q=0.180*5/2*R*155K=0.180*5/2*8,315*155K= 579,97 J

and as i said q=deltaE during the final heating so, deltaE=579,97 J

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