Question 6.5: Problem: An insulated cylinder fitted with a piston contains...
Problem: An insulated cylinder fitted with a piston contains 5 kg of air at 500 kPa and 1000 K. The air expands in an adiabatic process until its volume doubles. Calculate the work done by the air.
Find: Work W done by air during expansion.
Known: Mass of air m = 5 kg, initial pressure P_1 = 500 kPa, initial temperature T_1 = 1000 K, final volume ν_2 = 2ν_1 , adiabatic process so Q_{12} = 0.
Assumptions: Air is an ideal gas with constant specific heats, the process is reversible and adiabatic so ∆s = 0
Governing equations:
Isentropic process (ideal gas, constant specific heats) \frac{T_2}{T_1}=\left\lgroup \frac{ν_1}{ν_2}\right\rgroup ^{(\gamma -1)}
First law ΔU=Q_{12}+W_{12}=Q_{12}+mc_ν(T_2-T_1)
Properties: Air at 1000 K has specific heat c_ν = 0.855 kJ / kgK (Appendix 4), specific heat ratio of air at 1000 K γ = 1.336 (Appendix 4).
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