The absolute temperature of a gas is increased four times while maintaining a constant volume. What happens to the pressure of the gas?

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The absolute temperature of a gas is increased four times while maintaining a constant volume. What happens to the pressure of the gas?

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Answer 1 · 2017-03-28T02:44:08

The pressure of the gas also increases by a factor of $4$ $4$ .

Explanation:

Since there is constant volume, we can use Gay-Lussac's Law:

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$ $P_1/T_1 = P_2/T_2$

The problem tells us that the temperature of the gas is increased by a factor of 4. So, we can make the substitution:

$T_{2} = 4 T_{1}$ $T_2 = 4T_1$

Now, use this substitution to find $P_{2}$ $P_2$ in terms of $P_{1}$ $P_1$ .

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$ $P_1/T_1 = P_2/T_2$

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{4 T_{1}} XXXX$ $P_1/T_1 = P_2/(4T_1) color(white)"XXXX"$ substitute $4 T_{1}$ $4T_1$ for $T_{2}$ $T_2$

$4 P_{1} = P_{2} XXXXX$ $4P_1 = P_2 color(white)"XXXXX"$ multiply both sides by $4 T_{1}$ $4T_1$

This means that $P_{2}$ $P_2$ is $4$ $4$ times $P_{1}$ $P_1$ , so we can say that when the temperature of a gas increases by a factor of $4$ $4$ , the pressure of the gas also increases by a factor of $4$ $4$ .

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The absolute temperature of a gas is increased four times while maintaining a constant volume. What happens to the pressure of the gas?

1 Answer

Explanation:

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