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.

$$V_2 = V_1 \left(\frac{P_1}{P_2}\right)^{1/n}$$ $$V_2 = V_1 \left(\frac{4000 \text{ kPa}}{230 \text{ kPa}}\right)^{1/1.4}$$ $$V_2 = V_1 (17.3913)^{0.7142857}$$ $$V_2 = V_1 (7.0010)$$

$$W = \frac{P_2 V_2 - P_1 V_1}{1-n}$$ $$W = \frac{(230 \text{ kPa}) (7.0010 V_1) - (4000 \text{ kPa}) V_1}{1-1.4}$$ $$W = \frac{1610.23 V_1 - 4000 V_1}{-0.4}$$ $$W = \frac{-2389.77 V_1}{-0.4}$$ $$W = 5974.43 V_1 \text{ kJ}$$

The work done by the gas during the expansion is $\boxed{\text{5974.43 } V_1 \text{ kJ}}$.
(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)
$P_1 = 0.15 \text{ MPa} = 150 \text{ kPa}$
$P_2 = 0.6 \text{ MPa} = 600 \text{ kPa}$
$T_1 = 30^\circC = 303.15 \text{ K