SATHEE: Heat and Thermodynamics 4 Question 7

Heat and Thermodynamics 4 Question 7

8. For a given gas at $1 a t m$ pressure, rms speed of the molecules is $200 m / s$ at $127^{\circ} C$ . At $2 a t m$ pressure and at $227^{\circ} C$ , the rms speed of the molecules will be

(2019 Main, 9 April I)

(a) $100 \sqrt{5} m / s$

(b) $80 m / s$

(d) $80 \sqrt{5} m / s$

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Solution:

Key Idea For a gas molecule,

$\begin{aligned} v_{r m s} = \sqrt{\frac{3 R T}{M}} \\ ∴ & v_{r m s} \propto \sqrt{T} \end{aligned}$

Let unknown rms speed be $v_{rms, 2}$

at $T_{2} = 227^{\circ} C ($ or $500 K)$

and at $T_{1} = 127^{\circ} C$ (or $400 K$ )

$v_{r m s, 1} = 200 m / s$

$∴$ Using the relation $v_{r m s} \propto \sqrt{T}$ , we can write

$\frac{v_{r m s, 2}}{v_{r m s, 1}} = \sqrt{\frac{T_{2}}{T_{1}}}$

Substituting these given values in Eq. (i), we get

$\begin{aligned} ∴ v_{r m s, 2} & = \sqrt{\frac{500}{400}} \times 200 m / s \\ = \frac{1}{2} \sqrt{5} \times 200 m / s = 100 \sqrt{5} m / s \end{aligned}$

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Heat and Thermodynamics 4 Question 7

8. For a given gas at $1 a t m$ pressure, rms speed of the molecules is $200 m / s$ at $127^{\circ} C$ . At $2 a t m$ pressure and at $227^{\circ} C$ , the rms speed of the molecules will be

Solution:

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Heat and Thermodynamics 4 Question 7

8. For a given gas at 1atm pressure, rms speed of the molecules is 200m/s at 127∘C. At 2atm pressure and at 227∘C, the rms speed of the molecules will be

Solution:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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8. For a given gas at $1 a t m$ pressure, rms speed of the molecules is $200 m / s$ at $127^{\circ} C$ . At $2 a t m$ pressure and at $227^{\circ} C$ , the rms speed of the molecules will be