Question

How does the ideal Ericsson cycle differ from the Carnot cycle?

Short answer

Answer: The main differences between the ideal Ericsson cycle and the Carnot cycle are the processes involved, with the Ericsson cycle having constant pressure cooling and heating processes, while the Carnot cycle has adiabatic expansions and compressions. Both cycles have the same efficiency as they operate between the same temperature reservoirs. However, the Ericsson cycle is more suited for practical heat engines and gas turbines due to its constant pressure processes, while the Carnot cycle is a theoretical cycle with ideal conditions that are practically impossible to achieve.

Step-by-step solution

Understand the Carnot Cycle

The Carnot cycle is a theoretical thermodynamic cycle that provides the maximum possible efficiency for a heat engine operating between temperature reservoirs at T1 (hot) and T2 (cold). It consists of four reversible processes: 1. Isothermal Expansion: The working gas expands isothermally (constant temperature) at T1, and the system absorbs heat Q1 from the hot reservoir. 2. Adiabatic Expansion: The gas expands adiabatically (no heat exchange) until its temperature drops to T2. 3. Isothermal Compression: The gas gets compressed isothermally at T2, and the system releases heat Q2 to the cold reservoir. 4. Adiabatic Compression: The gas gets compressed adiabatically until its temperature rises back to T1.

Understand the Ericsson Cycle

The Ericsson cycle is an ideal thermodynamic cycle consisting of four processes as well, but with slight differences compared to the Carnot cycle: 1. Isothermal Expansion: The gas expands isothermally at T1 while absorbing heat Q1 from the hot reservoir (same as the Carnot cycle). 2. Constant pressure or isobaric cooling: The gas expands at a constant pressure until its temperature drops to T2. During the expansion, the system loses heat Qc to the cooling reservoir. 3. Isothermal Compression: The gas gets compressed isothermally at T2 and releases heat Q2 to the cold reservoir (same as the Carnot cycle). 4. Constant pressure or isobaric heating: The gas is compressed at constant pressure until its temperature rises back to T1. During this process, the system absorbs heat from an external heating reservoir.

Compare efficiencies

The efficiency of both cycles is the same because the efficiency is determined by the temperature difference between the hot and cold reservoirs. The efficiency is given by (1 - T2/T1), where T1 and T2 are the temperatures of the hot and cold reservoirs, respectively. Since both cycles operate between the same temperature reservoirs, their efficiencies are the same.

Practical applications and comparison

The Carnot cycle is a theoretical cycle with ideal conditions, which makes it practically impossible to achieve in real-world applications since it assumes reversible processes and no energy losses. On the other hand, the Ericsson cycle is more realistic due to the constant pressure processes. It is more suited for practical heat engines and gas turbines as these processes are more achievable in real-world applications compared to the isentropic processes in the Carnot cycle. In summary, although the theoretical efficiencies of both cycles are the same, the Ericsson cycle is more applicable in real-world situations.