0.5 kg of methane is initially at 500 kPa and 25°C. The methane expands in an isothermal process until its final volume is twice its initial volume. Assuming the methane behaves as an ideal gas with constant specific heats, determine (a) the initial volume, (b) the final pressure, (c) the change in specific internal energy and (d) the change in specific enthalpy of the methane.
Given: m = 0.5 kg; P1 = 500 kPa; T1 = T2 = 25°C = 298 K (isothermal process); V2 = 2V1
For CH4, R = 0.5182 kJ/kg-K, cp = 2.2537 kJ/kg-K, cv = 1.7354 kJ/kg-K at 300 K
(a) From the ideal gas law: V1 = mRT1/P1 = (0.5 kg)(0.5182 kJ/kg-K)(298 K)/ 500 kPa
V1 = 0.154 m3
(b) Therefore, V2 = 2V1 = 0.309 m3
From the ideal gas law: P2 = mRT2/V2 = 250 kPa
(c) ?u = cv (T2 – T1) = (1.7354 kJ/kg-K) (25°C – 25°C) = 0 kJ/kg
(d)?h = cp (T2 – T1) = (2.2537 kJ/kg-K) (25°C – 25°C) = 0 kJ/kg
The isothermal process has no change in internal energy or enthalpy.
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