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.
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
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