A gas expands polytropically from a pressure of 4 MPa to 230 KPa. The polytropic expansion n= 1.4, calculate the work done by the gas during the expansion. Hint: use P1 to find V1.

BRA-T, let's knock this out. 3.1. A gas expands polytropically from a pressure of 4 MPa to 230 KPa. The polytropic expansion n= 1.4, calculate the work done by the gas during the expansion. Hint: use P1 to find V1. Given: P_1 = 4 MPa = 4000 kPa P_2 = 230 kPa n = 1.4 The problem asks to calculate the work done but does not provide the initial volume (V_1) or mass of the gas. The hint "use P1 to find V1" is insufficient as V_1 cannot be determined from P_1 alone. Therefore, the work done will be expressed in terms of V_1. Step 1: Express V_2 in terms of V_1 using the polytropic relation P_1 V_1^n = P_2 V_2^n. V_2 = V_1 ((P_1)/(P_2))^1/n V_2 = V_1 (4000 kPa230 kPa)^1/1.4 V_2 = V_1 (17.3913)^0.7142857 V_2 = V_1 (7.0010) Step 2: Calculate the work done by the gas using the polytropic work formula. W = (P_2 V_2 - P_1 V_1)/(1-n) W = (230 kPa) (7.0010 V_1) - (4000 kPa) V_11-1.4 W = (1610.23 V_1 - 4000 V_1)/(-0.4) W = (-2389.77 V_1)/(-0.4) W = 5974.43 V_1 kJ The work done by the gas during the expansion is 5974.43 V_1 kJ. (Note: A numerical value for V_1 is required for a specific numerical answer.) 3.2. Air undergoes a polytropic in a piston-cylinder assembly from P1 = 0.15 MPa, P2 = 0.6 MPa, and T1 = 30°C. Apply the ideal gas model if n=1.4. Specific heat capacity, Cp for air can be assumed to be 1.007 KJ/kg. Calculate: Given: Air (ideal gas) P_1 = 0.15 MPa = 150 kPa P_2 = 0.6 MPa = 600 kPa $T_1 = 30^ = 303.15 K