Physics

Physics

Problem

Assertion : In equation p=13αvrms2p = \frac{1}{3} \alpha v_{\text{rms}}^2 , the term α\alpha represents density of gas. Reason : vrms=3RTMv_{\text{rms}} = \sqrt{\frac{3RT}{M}} .
Intuitive explanation

The assertion claims α\alpha is density, but you need to check what the kinetic theory equation actually says. The key insight is to work backwards from the vrmsv_{\text{rms}} formula—substitute it into the pressure equation and see what α\alpha must be to make the result match the ideal gas law. This reveals whether α\alpha is truly density or something else, and whether the reason correctly supports the claim.

Intuitive explanation

The assertion claims α\alpha is density, but you need to check what the kinetic theory equation actually says. The key insight is to work backwards from the vrmsv_{\text{rms}} formula—substitute it into the pressure equation and see what α\alpha must be to make the result match the ideal gas law. This reveals whether α\alpha is truly density or something else, and whether the reason correctly supports the claim.

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