A balloon partially filled with helium has a volume of $30 \mathrm{~m}^{3}$ at the earth's surface where pressure is 76 cm Hg and temperature is $27^{\circ} \mathrm{C}$ . What will be the increase in volume of gas if balloon rises to a height, where pressure is 7.6 cm Hg and temperature is $-54^{\circ} \mathrm{C}$?

Question

Accepted Answer

ক. $189 \mathrm{~m}^{3}$

ব্যাখ্যা: আদর্শ গ্যাস সমীকরণ অনুযায়ী, $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$। 
এখানে, 
$P_1 = 76	ext{ cm Hg}$, $V_1 = 30	ext{ m}^3$, $T_1 = 27^\circ	ext{C} = 300	ext{ K}$ 
$P_2 = 7.6	ext{ cm Hg}$, $T_2 = -54^\circ	ext{C} = 219	ext{ K}$

সুতরাং, শেষ আয়তন: 
$V_2 = V_1 	imes \frac{P_1}{P_2} 	imes \frac{T_2}{T_1} = 30 	imes \left(\frac{76}{7.6}ight) 	imes \left(\frac{219}{300}ight) = 30 	imes 10 	imes 0.73 = 219	ext{ m}^3$।

আয়তন বৃদ্ধি = $V_2 - V_1 = 219	ext{ m}^3 - 30	ext{ m}^3 = 189	ext{ m}^3$।

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