A cylinder with a piston contains 0.200 mol of nitrogen at 1.70×10 5 Pa and 320

Question

A cylinder with a piston contains 0.200 mol of nitrogen at 1.70×105 Pa and 320 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.

Part A- Find the work done by the gas during the initial compression. In J

Part B- Find the heat added to the gas during the initial compression. In J

Part C- Find internal-energy change of the gas during the initial compression.. In J

Explanation / Answer

A)
Find initial volume:
P*V = n*R*T
1.7*10^5 * V = 0.2*8.314 * 320
V = 3.13*10^-3 m^3
W = P (change in volume)
= 1.7*10^5 * ( - 3.13*10^-3/2)
= - 266 J

B)
since volume is halfed , temperature will be halfed too
Tf = 320/2 = 160 K
Cp of N2 is 1.04 J/gK
m =number of moles * molar mass
= 0.2 * 28
= 5.6 gm
Q = m* Cp * (Tf -Ti)
= 5.6 * 1.04* (160 - 320)
= -932 J -266 J
= -1198 J

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