Is it possible to have a gas change both its temperature and pressure but not have it's volume change? If this is possible, make up a gas law problem that shows this occurrence.

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Yes, it is very much possible to change the pressure of a gas by varying its temperature. Higher the temperature, higher is the pressure exerted by the gas molecules on the walls of the container. In other words, Pressure varies directly as absolute temperature of a gas. This is Amontons’ law, or the pressure law (it is also sometimes called Gay-Lussac’s law, but this law popularly refers to his famous law of combined gaseous volumes). It states that volume remaining constant, the pressure exerted on a container's sides by an ideal gas is proportional to its absolute temperature.

Mathematically, P α T

Or, `(P_1)/(T_1) = (P_2)/(T_2) = ... = (P_n)/(T_n)`

An alternate statement of this law, more useful for P-T calculations, goes as: "Volume remaining constant, the pressure of a given mass of gas increases or decreases by the same fraction of its pressure at 0°C, per degree rise (or fall) in temperature". In line with the Charles’ law, this fraction is also equal to 1/273.

The explanation for such variation is that, as the temperature increases, the molecules in the gas move faster, impacting the gas’s container more frequently and exerting a greater force. This increases the pressure.

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