PRELIMINARY STAGE 2024
Contest 34
T.I. AMASS, Kumasi: 71 points (Winner)
Amenfiman SHS –40 pts
Tuobodom SHTS: 21 points
Contest 35
Accra Girls’ SHS: 39 points (Winner)
Notre Dame Girls’ SHS: 34 points
Aburi Girls’ SHS –27 pts
Contest 36
Anlo SHS: 69 points (Winner)
Tamale Islamic Science SHS –34 pts
Yendi SHS –28 pts
FIRST SET OF QUESTIONS
PREAMBLE
Consider an isothermal ideal gas process
FORMULA
Isothermal process formula:
$P_{1} \times V_{1} = P_{2} \times V_{2}$
1.Find final pressure if initial pressure is 20 Kpa, initial volume is $3.4\text{ dm}^{3}$ and final volume is $6.8\text{ dm}^{3}$
ANSWER: Final pressure = $10\text{ kPa}$
SOLUTION 1:
$P_1 = 20\text{ kPa}$
$V_1 = 3.4\text{ dm}^3$
$V_2 = 6.8\text{ dm}^3$
$P_2 = \dfrac{P_1 \times V_1}{V_2}$
$P_2 = \dfrac{20 \times 3.4}{6.8}$
$P_2 = \dfrac{20 \times 34}{68}$
$P_2 = \dfrac{20}{2}$
$P_2 = 10\text{ kPa}$
SOLUTION 2:
$P_1 \times V_1 = P_2 \times V_2$
$20 \times 3.4 = P_2 \times 6.8$
$68 = P_2 \times 6.8$
$P_2 = \dfrac{68}{6.8}$
$P_2 = \dfrac{68}{68\times10^{-1}}$
$P_2 = 10\text{ kPa}$
2.Find final volume if initial volume is $3.2\text{ dm}^{3}$, initial pressure is 25 KPa and final pressure is 5.0 kPa
ANSWER: Final volume = $16\text{ dm}^3$
SOLUTION 1:
$P_1 = 25\text{ kPa}$
$V_1 = 3.2\text{ dm}^3$
$P_2 = 5.0\text{ kPa}$
$V_2 = \dfrac{P_1 \times V_1}{P_2}$
$V_2 = \dfrac{25 \times 3.2}{5.0}$
$V_2 = \dfrac{25 \times 32\times10^{-1}}{5}$
$V_2 = 5 \times 32 \times10^{-1}$
$V_2 = 16\text{ dm}^3$
SOLUTION 2:
$P_1 \times V_1 = P_2 \times V_2$
$25 \times 3.2 = 5.0 \times V_2$
$80 = 5.0 \times V_2$
$V_2 = \dfrac{80}{5.0}$
$V_2 = 16\text{ dm}^3$
3.Find final pressure if initial pressure is 14 Kpa, initial volume is $4.5\text{ dm}^{3}$ and final volume is $1.5\text{ dm}^{3}$
ANSWER: Final pressure = $42\text{ kPa}$
SOLUTION 1:
$P_1 = 14\text{ kPa}$
$V_1 = 4.5\text{ dm}^3$
$V_2 = 1.5\text{ dm}^3$
$P_2 = \dfrac{P_1 \times V_1}{V_2}$
$P_2 = \dfrac{14 \times 4.5}{1.5}$
$P_2 = 14 \times 3$
$P_2 = 42\text{ kPa}$
SOLUTION 2:
$P_1 \times V_1 = P_2 \times V_2$
$14 \times 4.5 = P_2 \times 1.5$
$63 = P_2 \times 1.5$
$P_2 = \dfrac{63}{1.5}$
$P_2 = \dfrac{63}{15\times10^{-1}}$
$P_2 = \dfrac{21}{5} \times10^{1}$
$P_2 = 42\text{ kPa}$
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PRACTICE QUESTIONS
1. QUESTION: Find the final pressure if the initial pressure is 24 kPa, the initial volume is 3.5 dm³ and the final volume is 7.0 dm³, at constant temperature.
ANSWER: 12 kPa or $1.2\times10^{1}$ kPa
SOLUTION:
$P_1V_1 = P_2V_2$
$P_2 = \dfrac{P_1V_1}{V_2}$
$P_2 = \dfrac{24 \times 3.5}{7.0}$
$P_2 = \dfrac{24 \times 35\times10^{-1}}{7}$
$P_2 = 24 \times 5 \times10^{-1}$
$P_2 = 12\text{ kPa}$
2. QUESTION: Find the final volume if the initial volume is 2.4 dm³, the initial pressure is 45 kPa and the final pressure is 15 kPa, at constant temperature.
ANSWER: 7.2 dm³
SOLUTION:
$P_1V_1 = P_2V_2$
$V_2 = \dfrac{P_1V_1}{P_2}$
$V_2 = \dfrac{45 \times 2.4}{15}$
$V_2 = \dfrac{45 \times 24\times10^{-1}}{15}$
$V_2 = 3 \times 24 \times10^{-1}$
$V_2 = 7.2\text{ dm}^3$
3. QUESTION: Find the final pressure if the initial pressure is 125 kPa, the initial volume is 2.4 dm³ and the final volume is 1.2 dm³, at constant temperature.
ANSWER: 250 kPa or $2.5\times10^{2}$ kPa
SOLUTION:
$P_1V_1 = P_2V_2$
$P_2 = \dfrac{P_1V_1}{V_2}$
$P_2 = \dfrac{125 \times 2.4}{1.2}$
$P_2 = \dfrac{125 \times 24}{12}$
$P_2 = 125 \times 2$
$P_2 = 2.5\times10^{2}\text{ kPa}$
4. QUESTION: Find the final volume if the initial volume is 1.5 dm³, the initial pressure is 32 kPa and the final pressure is 64 kPa, at constant temperature.
ANSWER: 0.75 dm³ or $7.5\times10^{-1}$ dm³
SOLUTION:
$P_1V_1 = P_2V_2$
$V_2 = \dfrac{P_1V_1}{P_2}$
$V_2 = \dfrac{32 \times 1.5}{64}$
$V_2 = \dfrac{32 \times 15\times10^{-1}}{64}$
$V_2 = \dfrac{15}{2} \times10^{-1}$
$V_2 = 0.75\text{ dm}^3$
5. QUESTION: Find the final pressure if the initial pressure is 65 kPa, the initial volume is 2.2 dm³ and the final volume is 5.5 dm³, at constant temperature.
ANSWER: 26 kPa or $2.6\times10^{1}$ kPa
SOLUTION:
$P_1V_1 = P_2V_2$
$P_2 = \dfrac{P_1V_1}{V_2}$
$P_2 = \dfrac{65 \times 2.2}{5.5}$
$P_2 = \dfrac{143}{5.5}$
$P_2 = \dfrac{143}{55\times10^{-1}}$
$P_2 = \dfrac{13}{5} \times10^{1}$
$P_2 = 26\text{ kPa}$
6. QUESTION: Find the final volume if the initial volume is 9.0 dm³, the initial pressure is 12 kPa and the final pressure is 36 kPa, at constant temperature.
ANSWER: 3.0 dm³
SOLUTION:
$P_1V_1 = P_2V_2$
$V_2 = \dfrac{P_1V_1}{P_2}$
$V_2 = \dfrac{12 \times 9.0}{36}$
$V_2 = \dfrac{9}{3}$
$V_2 = 3.0\text{ dm}^3$
7. QUESTION: Find the final pressure if the initial pressure is 72 kPa, the initial volume is 4.8 dm³ and the final volume is 6.4 dm³, at constant temperature.
ANSWER: 54 kPa or $5.4\times10^{1}$ kPa
SOLUTION:
$P_1V_1 = P_2V_2$
$P_2 = \dfrac{P_1V_1}{V_2}$
$P_2 = \dfrac{72 \times 4.8}{6.4}$
$P_2 = \dfrac{72 \times 48}{64}$
$P_2 = \dfrac{72 \times 3}{4}$
$P_2 = 18 \times 3$
$P_2 = 54\text{ kPa}$
8. QUESTION: Find the final volume if the initial volume is 6.5 dm³, the initial pressure is 28 kPa and the final pressure is 91 kPa, at constant temperature.
ANSWER: 2.0 dm³
SOLUTION:
$P_1V_1 = P_2V_2$
$V_2 = \dfrac{P_1V_1}{P_2}$
$V_2 = \dfrac{28 \times 6.5}{91}$
$V_2 = \dfrac{182}{91}$
$V_2 = 2.0\text{ dm}^3$
9. QUESTION: Find the final pressure if the initial pressure is 36 kPa, the initial volume is 7.2 dm³ and the final volume is 2.4 dm³, at constant temperature.
ANSWER: 110 kPa or $1.1\times10^{2}$ kPa
SOLUTION:
$P_1V_1 = P_2V_2$
$P_2 = \dfrac{P_1V_1}{V_2}$
$P_2 = \dfrac{36 \times 7.2}{2.4}$
$P_2 = \dfrac{36 \times 72}{24}$
$P_2 = 36 \times 3$
$P_2 \approx 1.1\times10^{2}\text{ kPa}$
10. QUESTION: Find the final volume if the initial volume is 3.2 dm³, the initial pressure is 55 kPa and the final pressure is 22 kPa, at constant temperature.
ANSWER: 8.0 dm³
SOLUTION:
$P_1V_1 = P_2V_2$
$V_2 = \dfrac{P_1V_1}{P_2}$
$V_2 = \dfrac{55 \times 3.2}{22}$
$V_2 = \dfrac{55 \times 32\times10^{-1}}{22}$
$V_2 = \dfrac{5 \times 32}{2} \times10^{-1}$
$V_2 = 5 \times 16 \times10^{-1}$
$V_2 = 8.0\text{ dm}^3$
11. QUESTION: Find the final pressure if the initial pressure is 48 kPa, the initial volume is 3.6 dm³ and the final volume is 8.0 dm³, at constant temperature.
ANSWER: 22 kPa or $2.2\times10^{1}$ kPa
SOLUTION:
$P_1V_1 = P_2V_2$
$P_2 = \dfrac{P_1V_1}{V_2}$
$P_2 = \dfrac{48 \times 3.6}{8.0}$
$P_2 = \dfrac{48 \times 36\times10^{-1}}{8}$
$P_2 = 6 \times 36 \times10^{-1}$
$P_2 \approx 22\text{ kPa}$
12. QUESTION: Find the final volume if the initial volume is 1.8 dm³, the initial pressure is 75 kPa and the final pressure is 45 kPa, at constant temperature.
ANSWER: 3.0 dm³
SOLUTION:
$P_1V_1 = P_2V_2$
$V_2 = \dfrac{P_1V_1}{P_2}$
$V_2 = \dfrac{75 \times 1.8}{45}$
$V_2 = \dfrac{75 \times 18\times10^{-1}}{45}$
$V_2 = \dfrac{5 \times 18}{3} \times10^{-1}$
$V_2 = 5 \times 6 \times10^{-1}$
$V_2 = 3.0\text{ dm}^3$