The pressure of a given mass of gas changes from 200 Nm2 to 100 N m2, while its temperature drops from 127oC to - 73oC. Calculate the radio of the final volume of the gas to its initial volume.
A
2.4:1
B
2.0:1
C
1.2:1
D
1.0:1
E
1.0:2
Verified Correct Answer: D.
Physical Principles & Numerical Solution
To find the ratio of the final volume of the gas to its initial volume, we use the ideal gas law:
\(\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}\)
Rearranging gives:
\(\frac{V_2}{V_1} = \frac{P_1 T_2}{P_2 T_1}\)
Substituting the values:
- \( P_1 = 200 \, N/m^2 \)
- \( P_2 = 100 \, N/m^2 \)
- \( T_1 = 400.15 \, K \)
- \( T_2 = 200.15 \, K \)
We have:
\(\frac{V_2}{V_1} = \frac{200 \times 200.15}{100 \times 400.15}\)
Calculating the ratio:
\(\frac{V_2}{V_1} = \frac{40030}{40015} \approx 1.0:1\)
Thus, the ratio of the final volume of the gas to its initial volume is: 1.0:1
Source: Myschool Past Questions Archive (Record #25068)