In a Carnot cycle operating between 330°C and 35°C, the maximum and minimum pressures are 6 MPa and 0.25 MPa respectively. (Assume air to be working fluid). Given R = 0.287 kJ/kmol.K and Cp=1.005 kJ/kmol.K. Sketch the Carnot cycle on T-S diagram. Calculate the thermal efficiency.

2.1. Sketch the Carnot cycle on T – S diagram.

A Carnot cycle on a T-S (Temperature-Entropy) diagram is represented by a rectangle. • The two horizontal lines represent the isothermal processes (constant temperature), where heat is added ($T_H$) and rejected ($T_L$). • The two vertical lines represent the isentropic (adiabatic and reversible) processes (constant entropy), where the working fluid expands and compresses.

The cycle proceeds as follows:

1. Isothermal heat addition (1-2): A horizontal line from left to right at the higher temperature $T_H$, indicating an increase in entropy.
2. Isentropic expansion (2-3): A vertical line downwards, indicating a decrease in temperature from $T_H$ to $T_L$ at constant entropy.
3. Isothermal heat rejection (3-4): A horizontal line from right to left at the lower temperature $T_L$, indicating a decrease in entropy.
4. Isentropic compression (4-1): A vertical line upwards, indicating an increase in temperature from $T_L$ to $T_H$ at constant entropy, completing the cycle.

2.2. Calculate the thermal efficiency.

Step 1: Convert the given temperatures from Celsius to Kelvin. The hot reservoir temperature is $T_H = 330^\circ\text{C}$. The cold reservoir temperature is $T_L = 35^\circ\text{C}$. To convert to Kelvin, add 273.15. $T_H = 330 + 273.15 = 603.15 \text{ K}$ $T_L = 35 + 273.15 = 308.15 \text{ K}$

Step 2: Apply the formula for the thermal efficiency of a Carnot cycle. The thermal efficiency ($\eta_{th}$) of a Carnot cycle is given by: $\eta_{th} = 1 - \frac{T_L}{T_H}$

Step 3: Substitute the values and calculate the efficiency. $\eta_{th} = 1 - \frac{308.15 K}{603.15 K}$ $\eta_{th} = 1 - 0.510897$ $\eta_{th} = 0.489103$

Step 4: Express the efficiency as a percentage. $\eta_{th} = 0.489103 \times 100\% = 48.91\%$

The thermal efficiency of the Carnot cycle is: \boxed{48.91%}