Question:
What is the correct equation that relates kinetic energy (\(E_{\text{ke}}\)) and pressure (\(P\)) of one mole of an ideal gas?
- (V = Volume)
What is the correct equation that relates kinetic energy (\(E_{\text{ke}}\)) and pressure (\(P\)) of one mole of an ideal gas?
- (V = Volume)
Show Hint
The kinetic energy of an ideal gas is related to pressure using:
\[
P V = \frac{2}{3} E_{\text{ke}}
\]
This formula comes from the kinetic theory of gases, considering molecular motion and collisions.
Updated On: May 5, 2026
- \( P = \frac{2E_{\text{ke}}}{3V} \)
- \( P = \frac{3V}{2E_{\text{ke}}} \)
- \( P = \frac{3V^2}{2E_{\text{ke}}} \)
- \( P = \frac{2(E_{\text{ke}})^2}{3V} \)
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The Correct Option is A
Solution and Explanation
To find the correct equation relating the kinetic energy E_{\text{ke}} and pressure P of one mole of an ideal gas, we use kinetic theory.
- The kinetic energy of one mole of an ideal gas is: E_{\text{ke}} = \frac{3}{2} RT
- From the ideal gas equation: PV = RT
- Substitute RT from above: RT = \frac{2}{3}E_{\text{ke}}
- Putting this into P = \frac{RT}{V}: P = \frac{2E_{\text{ke}}}{3V}
Final Answer: P = \frac{2E_{\text{ke}}}{3V}
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