Question
Download Solution PDFThe relationship between two specific heats CP and CV is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- A perfect gas is also an Ideal gas, which follows the Ideal gas equation of states i.e. PV = mRT all temperature.
- where, P = pressure of gas, V = volume occupied, m = mass of a gas, R = universal gas constant.
- The universal gas constant (R) is the difference between specific heat constants for constant pressure (Cp) and constant volume (Cv)
- i.e. R = Cp - Cv
A real gas behaves as an Ideal gas at low pressure and very high temperature. Air is a perfect gas.
Gases that obey the gas laws (Charles law, Boyles law, and Universal Gas Law) are called ideal gases.
Boyle’s, Charles’, and Gay Lussac's Laws describe the basic behavior of fluids with respect to volume, pressure, and temperature.
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Gay Lussac’s Law |
It states that at constant volume, the pressure of a fixed amount of a gas varies directly with temperature. P ∝ T \(\frac{P}{T} = Const\) |
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Boyle's Law |
For a fixed mass of gas at a constant temperature, the volume is inversely proportional to the pressure. \(P\propto \frac{1}{V}\) PV = constant (If the temperature remains constant, the product of pressure and volume of a given mass of a gas is constant.) |
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Charles' Law |
For a fixed mass of gas at constant pressure, the volume is directly proportional to the Kelvin temperature. \(V\propto T \ or, \ \frac{V}{T} = Const\) |
The Combined gas law or General Gas Equation is obtained by combining Boyle's Law, Charles's law, and Gay-Lussac's Law. It shows the relationship between the pressure, volume, and temperature for a fixed mass (quantity) of gas:
\(\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}\)
\({C_P} - {C_V} = \frac{R}{J}\) is valid for a perfect gas only.
Last updated on Mar 26, 2025
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