The pressure of a given mass of gas changes from 200 Nm\(^{-2}\) to 100 Nm\(^{-2}\), while its temperature drops from 127°C to -73°C. Calculate the ratio of the final volume of the gas to its initial volume.
A
2.0: 1
B
2.4: 1
C
1.0: 1
D
1.2: 1
Verified Correct Answer: C.
Physical Principles & Numerical Solution
P\(_1\) = 200 Nm\(^{-2}\); P₂ = 100 Nm\(^{-2}\); T\(_1\) = 127 + 273 = 400 K; T\(_2\) = -73 + 273 = 200 K; \(\frac{V_2}{V_1}\) = ?
\(\frac{P_1V_1 }{ T_1} = \frac{P_2V_2 }{T_2}\)
\(\frac{V_2}{V_1}\) = \(\frac{P_1 T_2}{P_2 T_1}\)
\(\frac{V_2}{V_1}\) = \(\frac{200 \times 200}{100 \times 400}\) = \(\frac{1}{1}\) = 1: 1
Source: WAEC / JAMB / NECO Classroom Archive (Record #76355)