The temperature of a cubicle with height of 300 cm increases from 7°C to 27°C from night to day time. If there are 6.023×1025 6.023 imes 10^{25} number of molecules of gas available inside that cubicle, what will be the change in pressure due to temperature variation?

Question

The temperature of a cubicle with height of 300 cm increases from 7°C to 27°C from night to day time. If there are 6.023×1025 6.023 	imes 10^{25} number of molecules of gas available inside that cubicle, what will be the change in pressure due to temperature variation?

Accepted Answer

গ. 615.8 Pa

ব্যাখ্যা: ঘনকাকার প্রকোষ্ঠের (cubicle) বাহুর দৈর্ঘ্য $L = 300	ext{ cm} = 3	ext{ m}$
আয়তন $V = L^3 = 3^3 = 27	ext{ m}^3$
অণুর সংখ্যা $N = 6.023 	imes 10^{25}$, তাই মোলার সংখ্যা $n = \frac{N}{N_A} = \frac{6.023 	imes 10^{25}}{6.023 	imes 10^{23}} = 100	ext{ mol}$
তাপমাত্রার পরিবর্তন $\Delta T = 27^\circ	ext{C} - 7^\circ	ext{C} = 20	ext{ K}$

চাপের পরিবর্তন:
$$\Delta P = \frac{n R \Delta T}{V} = \frac{100 	imes 8.314 	imes 20}{27} = \frac{16628}{27} \approx 615.85	ext{ Pa} \approx 615.8	ext{ Pa}$$

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