The gas inside of a container exerts $12 P a$ $12 Pa$ of pressure and is at a temperature of $360^{o} K$ $360 ^o K$ . If the pressure in the container changes to $64 P a$ $64 Pa$ with no change in the container's volume, what is the new temperature of the gas?

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The gas inside of a container exerts $12 P a$ $12 Pa$ of pressure and is at a temperature of $360^{o} K$ $360 ^o K$ . If the pressure in the container changes to $64 P a$ $64 Pa$ with no change in the container's volume, what is the new temperature of the gas?

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Answer 1 · 2017-08-18T01:45:32

$T_{2} = 1920$ $T_2 = 1920$ $K$ $"K"$

Explanation:

We're asked to find the final temperature of a gas, given some pressure and temperature information.

To do this, we can use the pressure-temperature relationship of gases, illustrated by Gay-Lussac's law:

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$ $(P_1)/(T_1) = (P_2)/(T_2)" "$ (constant volume and quantity of gas)

where

$P_{1}$ $P_1$ and $P_{2}$ $P_2$ are the initial and final pressures of the gas
$T_{1}$ $T_1$ and $T_{2}$ $T_2$ are the initial and final absolute temperatures of the gas (which must be in Kelvin)

We know:

$P_{1} = 12$ $P_1 = 12$ $Pa$ $"Pa"$
$P_{2} = 64$ $P_2 = 64$ $Pa$ $"Pa"$
$T_{1} = 360$ $T_1 = 360$ $K$ $"K"$
$T_{2} = ?$ $T_2 = ?$

Plugging these in:

$\frac{12 l Pa}{360 l K} = \frac{64 l Pa}{T_{2}}$ $(12color(white)(l)"Pa")/(360color(white)(l)"K") = (64color(white)(l)"Pa")/(T_2)$

$color(red)(ulbar(|stackrel(" ")(" "T_2 = 1920color(white)(l)"K"" ")|)$

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The gas inside of a container exerts $12 P a$ $12 Pa$ of pressure and is at a temperature of $360^{o} K$ $360 ^o K$ . If the pressure in the container changes to $64 P a$ $64 Pa$ with no change in the container's volume, what is the new temperature of the gas?

1 Answer

Explanation:

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The gas inside of a container exerts 12 Pa12Pa12 Pa of pressure and is at a temperature of 360 ^o K360oK360 ^o K. If the pressure in the container changes to 64 Pa64Pa64 Pa with no change in the container's volume, what is the new temperature of the gas?

1 Answer

Explanation:

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The gas inside of a container exerts $12 P a$ $12 Pa$ of pressure and is at a temperature of $360^{o} K$ $360 ^o K$ . If the pressure in the container changes to $64 P a$ $64 Pa$ with no change in the container's volume, what is the new temperature of the gas?