The data listed below are claimed for power cycles operating...

The data listed below are claimed for power cycles operating between hot and cold reservoirs at $1000 \mathrm{~K}$ and $400 \mathrm{~K}$, respectively. For each case determine whether such a cycle is in keeping with the first and second laws of thermodynamics. (a) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=160 \mathrm{~kJ}, Q_{\mathrm{C}}=140 \mathrm{~kJ}$. (b) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=180 \mathrm{~kJ}, Q_{\mathrm{C}}=120 \mathrm{~kJ}$. (c) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=170 \mathrm{~kJ}, Q_{\mathrm{C}}=140 \mathrm{~kJ}$. (d) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=200 \mathrm{~kJ}, Q_{\mathrm{C}}=100 \mathrm{~kJ}$.

The data listed below are claimed for power cycles operating between hot and cold reservoirs at $1000 \mathrm{~K}$ and $400 \mathrm{~K}$, respectively. For each case determine whether such a cycle is in keeping with the first and second laws of thermodynamics.
(a) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=160 \mathrm{~kJ}, Q_{\mathrm{C}}=140 \mathrm{~kJ}$.
(b) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=180 \mathrm{~kJ}, Q_{\mathrm{C}}=120 \mathrm{~kJ}$.
(c) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=170 \mathrm{~kJ}, Q_{\mathrm{C}}=140 \mathrm{~kJ}$.
(d) $Q_{\mathrm{H}}=300 \mathrm{~kJ}, W_{\text {cycle }}=200 \mathrm{~kJ}, Q_{\mathrm{C}}=100 \mathrm{~kJ}$.

Key Concepts

First Law of Thermodynamics

The first law of thermodynamics, also known as the energy conservation law, states that energy cannot be created or destroyed but only transformed or transferred. In cyclic processes, this principle is applied by ensuring that the total heat input into the system equals the sum of the work output and the heat rejected. In evaluating power cycles, one checks if the supplied energy (heat from the hot reservoir) matches the energy removed as work and rejected heat, maintaining balance.

Second Law of Thermodynamics

The second law of thermodynamics defines the direction of energy transfers and introduces the concept of entropy, indicating that some energy must be degraded in quality during each energy conversion process. It sets limits on the achievable efficiency of heat engines. In these cycles, the law asserts that not all the heat input can be converted into work, and it must be ensured that any claimed cycle does not violate the entropy balance of the system.

Carnot Efficiency

Carnot efficiency represents the maximum possible efficiency that any heat engine operating between two reservoirs can achieve, defined by the temperatures of the hot and cold reservoirs (expressed as 1 - T_c/T_h). This concept is crucial in determining whether a power cycle can theoretically operate under the claimed conditions, as any real cycle must have an efficiency lower than or equal to the Carnot limit.

Transcript

Please give Ace some feedback