SATHEE: Heat and Thermodynamics 4 Question 13

Heat and Thermodynamics 4 Question 13

15. $A 15 g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ} C$ . Amount of heat transferred to the gas, so that rms velocity of molecules is doubled is about

(Take, $R = 8.3 J / K$ - mol)

(2019 Main, 9 Jan II)

(a) $10 k J$

(b) $0.9 k J$

(d) $6 k J$

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Solution:

We know that from kinetic theory of gases,

$V_{r m s} = \sqrt{\frac{3 R T}{M}} or V_{r m s} \propto \sqrt{T}$

where, $R$ is gas constant, $T$ is temperature and $M$ is molecular mass of a gas.

Here, to double the $v_{r m s}$ , temperature must be

4 times of the initial temperature.

$∴$ New temperature,

$\begin{aligned} T_{2} = 4 \times T_{1} \\ As, T_{1} = 27^{\circ} C = 300 K \\ ∴ T_{2} = 4 \times 300 = 1200 K \end{aligned}$

As, gas is kept inside a closed vessel.

$\begin{aligned} ∴ Q & = n C_{V} \cdot d T \\ = \frac{15}{28} \times \frac{5 R}{2} (1200 - 300) \\ [As, n = \frac{m}{M} = \frac{15}{28} for nitrogen] \\ = \frac{15}{28} \times \frac{5}{2} \times 8.3 \times 900 \end{aligned}$

[Given, $R = 8.3 J / K - m o l e$ ]

$or Q = 10004.4 J ≃ 10 k J$

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Heat and Thermodynamics 4 Question 13

15. $A 15 g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ} C$ . Amount of heat transferred to the gas, so that rms velocity of molecules is doubled is about

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

Heat and Thermodynamics 4 Question 13

15. A15g mass of nitrogen gas is enclosed in a vessel at a temperature 27∘C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled is about

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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15. $A 15 g$ mass of nitrogen gas is enclosed in a vessel at a temperature $27^{\circ} C$ . Amount of heat transferred to the gas, so that rms velocity of molecules is doubled is about