Problem

In a system the volume and mass are kept constant. The initial temperature of the system is \( 120^{\circ} \mathrm{C} \) and the pressure is \( 61.2 \mathrm{~atm} \). If the temperature changes to \( -14^{\circ} \mathrm{C} \) what is the pressure?

Answer

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Answer

3. Calculate the new pressure: \(P_2 = \frac{P_1 T_2}{T_1} = \frac{61.2\mathrm{~atm} \cdot 259.15\mathrm{~K}}{393.15\mathrm{~K}}\)

Steps

Step 1 ：1. Apply Gay-Lussac's Law: \(\frac{P_1}{T_1} = \frac{P_2}{T_2}\)

Step 2 ：2. Convert temperatures to Kelvin: \(T_1 = 393.15\mathrm{~K},~ T_2 = 259.15\mathrm{~K}\)

Step 3 ：3. Calculate the new pressure: \(P_2 = \frac{P_1 T_2}{T_1} = \frac{61.2\mathrm{~atm} \cdot 259.15\mathrm{~K}}{393.15\mathrm{~K}}\)

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