Is the Ideal Gas Law Applicable to Non-Isothermal Processes? | Homework Question

In summary, the ideal gas law, PV = mRT, can be applied to any process, including polytropic processes, as it is an equation of state that relates pressure, volume, and temperature. For a polytropic process, the equation only tells you what remains constant, and the temperature must change to maintain the equation.
  • #1
SherlockOhms
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Homework Statement


Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally? I mean, can it not be applied to a polytropic process, PVn = k.

Homework Equations


See above.

The Attempt at a Solution


N.A.
 
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  • #2
SherlockOhms said:
Is the ideal gas law, PV = mRT, only applicable to processes which are carried out isothermally?
No. It is an equation of state: it relates P, V, and T (assuming n fixed). It is valid everywhere (you can't have an ideal gas at pressure ##P_1## occupying volume ##V_1##, and measure temperature ##T_1##, and have the same amount of an ideal gas also at ##P_1## and ##V_1## and measure ##T_2 \neq T_1##).

For a polytropic process, the equation only tells you what remains constant during the process. In the formulation ##PV^\gamma = \text{const.}##, then ##T## must change when ##P## and ##V## change, such that ##PV = nRT## is maintained.
 
  • #3
Got it. Thanks for that.
 

Related to Is the Ideal Gas Law Applicable to Non-Isothermal Processes? | Homework Question

1. What is the Ideal Gas Law?

The Ideal Gas Law is a mathematical formula that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin.

2. Why is the Ideal Gas Law important?

The Ideal Gas Law is important because it allows scientists to predict the behavior of gases under different conditions. It is used in various fields of science, such as chemistry, physics, and engineering, to calculate and understand the properties of gases.

3. What are the assumptions of the Ideal Gas Law?

The Ideal Gas Law assumes that the gas molecules have negligible volume, there are no intermolecular forces between the gas molecules, and the collisions between gas molecules and the container walls are perfectly elastic. It also assumes that the gas is at low pressure and high temperature.

4. How is the Ideal Gas Law derived?

The Ideal Gas Law is derived from combining the three gas laws: Boyle's Law, Charles's Law, and Avogadro's Law. These laws describe the relationships between pressure and volume, volume and temperature, and volume and number of moles, respectively. By combining these laws, we can obtain the Ideal Gas Law equation.

5. Can the Ideal Gas Law be applied to real gases?

No, the Ideal Gas Law can only be applied to ideal gases, which do not exist in real life. Real gases deviate from ideal behavior at high pressures and low temperatures. To account for these deviations, scientists have developed other gas laws, such as the Van der Waals equation, that can be used for real gases.

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