Question

A sample of an ideal gas (γ=1.5) is compressed adiabatically from a volume of 150 cm³ to 50 cm³. The initial pressure and the initial temperature are 150 kPa and 300 K. Find (a) the number of moles of the gas in the sample, (b) the molar heat capacity at constant volume, (c) the final pressure and temperature, (d) the work done by the gas in the process and (e) the change in internal energy of the gas.

Answer 1

PV = nRT
Given P = 150 KPa = 150 × 10³ Pa, V = 150 cm³ = 150 × 10^–6 m³, T = 300 k

= 779.422 × 10³ Pa ≈ 780 KPa

(d) ΔQ = W + ΔU or W = –ΔU [ΔU = 0, in adiabatic]
= – nC_VdT = – 0.009 × 16.6 × (520 – 300) = – 0.009 × 16.6 × 220 = – 32.8 J ≈ – 33 J
(e) ΔU = nC_VdT = 0.009 × 16.6 × 220 ≈ 33 J