5 exercises on Gay-Lussac laws (with solutions)

On this page you will find a collection of exercises on the Laws of Gay-Lussac.
These laws, formulated by French chemist and physicist Joseph Louis Gay-Lussac in the early 19th century, describe the relationship between pressure, volume and temperature of gases, which are fundamental for understanding everyday phenomena and for practical applications ranging from meteorology to engineering.

Through these exercises, you will have the opportunity to apply the theoretical concepts you have learned and to develop a deeper understanding of the laws governing thermodynamics.
Each exercise is accompanied by a detailed explanation and solution steps, highlighting the physical laws and mathematical formulas used.

This collection is designed for students, teachers, and physics enthusiasts who want to deepen their understanding of gas laws and their applications.
We hope that it will be useful in your course of study and provide you with a solid foundation to confidently face the challenges posed by thermodynamics. Good luck with your work!

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Exercises on the laws of Gay-Lussac

On the first law of Gay-Lussac

A vessel equipped with a moving piston contains a volume of an unknown gas equal to $V_1 = 2.0 \ m^3$ at the temperature $T_1 = 300 \ K$ . If the vessel is left in the Sun, the temperature increases to $T_2 = 360 \ K$ and the gas begins to expand while maintaining constant pressure

Calculate the final volume $V_2$

Solution

On the second law of Gay-Lussac

A closed vessel contains an unknown gas at the pressure $P_1 = 2.0 \cdot 10^3 \ Pa$ and the temperature $T_1 = 300 \ K$ . The vessel is left in the Sun the temperature increases to $T_2 = 360 \ K$ and the pressure increases to $P_2$ . If the volume remains constant

Calculate the final pressure $P_2$

Solution

On the calculation of temperature

A gas, free to expand at constant pressure, triples its volume when it reaches a temperature $T_2 = 500 \ K$

Calculate the initial temperature $T_1$

Solution

On Gay-Lussac's first law for two gases in two vessels

Two unknown gases at the same initial temperature $T_{1,A} = T_{1,B} = T_1$ are contained inside two vessels equipped with a moving piston and are free to expand at constant pressure. Both are heated to the same temperature $T_{2,A} = T_{2,B} = T_2$ . The gas on the left (green) quadruples its volume while the gas on the right (red) reaches a volume $V_{2,B} = 42.2 \ m^3$

Calculate the initial volume of the gas $B$

Solution

On Gay-Lussac's second law and the calculation of temperature

A vessel contains an unknown gas at the pressure $P_1 = 2.0 \cdot 10^3 \ Pa$ and the temperature $T_1 = 340 \ K$ . If the gas is heated to a constant volume and reaches a pressure $P_2 = 4.0 \cdot 10^3 \ Pa$

Calculate the final temperature $T_2$

Solution

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