Which equation represents Gay-Lussac's law for a gas at constant volume?

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Multiple Choice

Which equation represents Gay-Lussac's law for a gas at constant volume?

Explanation:
When the volume is fixed, a gas’s pressure rises directly with its absolute temperature. This is Gay-Lussac’s law in action: as temperature increases (measured in Kelvin), pressure increases proportionally, so the ratio of pressure to temperature stays the same. The equation P1/T1 = P2/T2 captures that direct proportionality at constant volume, with temperature in Kelvin to keep the relationship linear. Think of it as the gas particles colliding with the container walls more vigorously as they heat up, leading to more pressure, and this increase happens in direct proportion to temperature when the space the gas can move in doesn’t change. This differs from other forms you might see: the full PV = nRT describes all four variables together; PV = constant with changing V relates to constant temperature (Boyle’s law); V as a function of T with constant pressure (V1/T1 = V2/T2) is Charles’ law. But for a fixed volume, the simplest, exact relation between pressure and temperature is P1/T1 = P2/T2, assuming temperature is in Kelvin.

When the volume is fixed, a gas’s pressure rises directly with its absolute temperature. This is Gay-Lussac’s law in action: as temperature increases (measured in Kelvin), pressure increases proportionally, so the ratio of pressure to temperature stays the same. The equation P1/T1 = P2/T2 captures that direct proportionality at constant volume, with temperature in Kelvin to keep the relationship linear.

Think of it as the gas particles colliding with the container walls more vigorously as they heat up, leading to more pressure, and this increase happens in direct proportion to temperature when the space the gas can move in doesn’t change.

This differs from other forms you might see: the full PV = nRT describes all four variables together; PV = constant with changing V relates to constant temperature (Boyle’s law); V as a function of T with constant pressure (V1/T1 = V2/T2) is Charles’ law. But for a fixed volume, the simplest, exact relation between pressure and temperature is P1/T1 = P2/T2, assuming temperature is in Kelvin.

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