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Entropy Calculations for Ideal Gases
For a closed system, the first law provides:
dU = dQ + dW
If the process of change occurs under reversible conditions then the above equation becomes:
d ( H − PV) = TdS − PdV
dH − PdV − VdP= TdS − PdV ............(4.18)
However for an ideal gas: dH = CigpdT .....(4.19)
Thus combining eqns. 4.18 and 4.19:
.....(4.20)
Integrating between an initial (T0, P0) and any final (T, P):
.....(4.21)
The last equation provides a direct expression for computing entropy change between two states for an ideal gas.
For the special case of a reversible adiabatic dQ = 0; hence dS= 0. Thus:
For constant CPig , it follows that: 
.....(4.22)
One may note that eqn. 4.22 provides the same relation as obtained by the Fist Law analysis as in eqn. 3.18.
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FAQs on Entropy Calculations for Ideal Gases - Thermodynamics - Mechanical Engineering
| 1. What is entropy and how is it calculated for ideal gases? |  |
Ans. Entropy is a thermodynamic property that describes the level of disorder or randomness in a system. For ideal gases, the entropy can be calculated using the equation:
$$
S = nR\ln\left(\frac{V}{V_0}\right)
$$
where S is the entropy, n is the number of moles of the gas, R is the gas constant, V is the volume of the gas, and V0 is a reference volume.
| 2. How does the entropy of an ideal gas change with temperature? | |
Ans. The entropy of an ideal gas increases with temperature. This is because as the temperature increases, the molecules of the gas gain more kinetic energy and move more rapidly, leading to a higher level of disorder and randomness in the system. Thus, the entropy increases as the gas becomes more disordered.
| 3. Can the entropy of an ideal gas be negative? | |
Ans. No, the entropy of an ideal gas cannot be negative. Entropy is a measure of disorder, and since disorder cannot be negative, the entropy of an ideal gas is always non-negative. It can only take a value of zero when the gas is in a perfectly ordered state, which is not typically observed in practice.
| 4. How does the entropy of an ideal gas change with pressure? | |
Ans. The entropy of an ideal gas does not depend on pressure. The entropy is solely influenced by the temperature and volume of the gas. Changes in pressure do not affect the level of disorder or randomness in the system, and therefore do not impact the entropy.
| 5. What is the significance of entropy in thermodynamics and engineering? | |
Ans. Entropy is a fundamental concept in thermodynamics and engineering. It helps to quantify the energy dispersal and level of disorder in a system. It plays a crucial role in various engineering applications, such as heat transfer, combustion, and power generation. Understanding and controlling entropy is essential for optimizing processes and improving the efficiency of engineering systems.
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