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^\circC =127+273 = 400K, T\(_2\) = −73^\circC = −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.