Question

6. One can store energy by compressing air, and then later use it to power a turbine to create energy when needed However, you have to heat the room temperature compressed air to make this effective. You can avoid this if you initially compress the air under adiabatic conditions, so the gas is already hot when you need it to generate electricity This is called adiabatic compressed air energy storage (CAES). Inside a typical power plant, 5.8x10° kg of N2 gas is at 25 °C is compressed from atmospheric to pressure into a volume of 300,000 m3 (they use abandoned salt mines) The process is done reversibly and adiabatically. What is Aq, n, Vi, Pf, ΔΤ, Δυ, Aw, and AH and for this process? (Cp.m (16 pts) 29.12 J/K/mol and Cvm 20.80 J/K/mol for N2). Assume perfect gas behavior.

Answer 1

Given that amount of N_2 = 5.8 times 1066 kg = 5.8 times 10^6 times 10^3 g = 5.8 2 10^9 g molecule wt of N_2 = 28 g/mol number of mol N_2 = 5.8 times 10^9/28 n = 2.07 times 10^8 mol initial temperature (T_i) = 25 degree C = 25 + 273 = 298 k initial pressure (Pi) = 1 atm final volume (v_f) = 3 times 10^6 m^3 C_p_1 m = 29.12 J/k/mol C_v_1 m = 20.80 J/k/mol (i) since process is adiabatic so heat exchange is zero i e Delta q = 0 (ii) number of moles of N_2 (n) is 2.07 times 10^8 mol (calculated above) (iii) since gas behavior ideal so P_1 V_1 = n R T_1 rightarrow 1 times v_i = 2.07 times 10^8 times 0.0821 times 298 rightarrow V_i = 50.64 times 1068 l = 50.64 times 10^8/10^3 m^3 v_i = 5064 times 10^5 m^3 (iv) x = c_p/c_v = 29.12/20.80 = 1.4