Question

An expansion process on a diatomic ideal gas (C_v = 5/2 R), has a linear path between the initial and final coordinates on a pV diagram. The coordinates of the initial state are : the pressure is 300 kPa, the volume is 0.08 m³ and the temperature is 390 K. The final pressure is 90kPa and the final temperature is 320 K. The change in the internal energy of the gas, in SI units, is closest to:

• A. –11, 000
• B. –6500
• C. 11, 000
• D. Zero

Answer 1

Answer: (A)

–11, 000

Answer 2

DU = nC_v DT

= n$\frac{5}{2}R$ (T_f – T_i)

n = $\frac{P_{1}V_{1}}{RT_{1}}$

DU = $\frac{P_{1}V_{1}}{RT_{1}}$ × $\frac{5}{2}$R (T₂ – T₁)

= $\frac{300 \times 10^{3} \times 0.08}{390}$×$\frac{5}{2}$ (320 – 390)

= $\frac{15 \times 10^{3} \times 0.08 \times 5}{39}$ × (–70)

= – $\frac{0.40}{39}$ × 15 × 10³ × 70

= – $\frac{40}{39}$×150 × 70

= – $\frac{40}{39}$×10500

DU = –11000 Joule