Question

An ideal gas within a piston-cylinder assembly executes a Carnot power cycle. The isothermal compression occurs at 300 K from 90 kPa to 120 kPa. If the thermal efficiency is 60%, determine;

a) The temperature of the isothermal expansion, in K
b) The net work developed, in kJ/kmol of gas.

Answer 1

The temperature of the isothermal expansion in a Carnot power cycle can be calculated using the formula, while the net work developed in the cycle is calculated using the thermal efficiency. For this specific scenario, the temperature of the isothermal expansion is 400 K and the net work is Q_h * 0.40.

Step-by-step explanation:

In a Carnot power cycle, the compression occurs isothermally at a temperature of 300 K. The temperature of the isothermal expansion can be found using the formula:

T_expansion = (T_compression * P_compression) / P_expansion

Given that the temperature of the compression is 300 K, the pressure of the compression is 120 kPa, and the pressure of the expansion is 90 kPa, we can calculate the temperature of the expansion as follows:

T_expansion = (300 K * 120 kPa) / 90 kPa = 400 K

The net work developed in the cycle can be found using the formula:

Net Work = Q_h * (1 - Efficiency)

Given that the thermal efficiency is 60% and the net work is expressed in kJ/kmol of gas, we can calculate the net work as follows:

Net Work = Q_h * (1 - 0.60) = Q_h * 0.40