If the temperature of a fixed amount of a gas is doubled at constant volume, what happens to the pressure?
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If the temperature of a fixed amount of a gas is doubled at constant volume, according to Gay-Lussac's Law, which is one of the gas laws, the pressure of the gas will also double. This relationship between temperature and pressure in a gas at constant volume is described by the formula:
\( P \propto T \)
where: - \( P \) represents the pressure of the gas - \( T \) represents the absolute temperature of the gas (measured in Kelvins) - \( \propto \) indicates proportionality
So, if you start with a certain pressure, say \( P_1 \), at a temperature \( T_1 \), and then you double the temperature to \( 2T_1 \) (while keeping the volume constant), the new pressure \( P_2 \) will be:
\( P_2 = 2P_1 \)
This means the pressure of the gas will be twice as much as the original pressure, assuming there are no changes in the amount of gas (moles) and that the gas behaves ideally.