The pressure of a given mass of a gas changes from 300Nm\(^{-2}\) to 120Nm\(^{-2}\) while the temperature drops from 127°C to -73°C. The ratio of the final volume to the initial volume is
- 2 : 5
-
5 : 4
- 4 : 5
- 5 : 2
The correct answer is: B
Explanation
To find the ratio of the final volume to the initial volume of a gas when both pressure and temperature change, we can use the Ideal Gas Law, which states that
\(\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}\)
P\(_1\) = 300N/m\(^2\) V\(_1\) = ?, V\(_2\) = ?, T\(_1\) = 127°C =127+273 = 400K, T\(_2\) = −73°C = −73 + 273 = 200K
P\(_2\) = 120N/m\(^2\)
Using the Ideal Gas Law, we can rearrange it to find the ratio of volumes:
= \(\frac{V_2}{V_1} = \frac{P_1T_2}{P_2T_1}\)
= \(\frac{V_2}{V_1} = \frac{300 \times 200}{120 \times 400}\) = \(\frac{5}{4}\)
Therefore, V\(_2\) : V\(_1\) = 5 : 4.
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