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 ***** 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]
= – nCVdT = – 0.009 × 16.6 × (520 – 300) = – 0.009 × 16.6 × 220 = – 32.8 J ≈ – 33 J
(e) ΔU = nCVdT = 0.009 × 16.6 × 220 ≈ 33 J