# The gas inside of a container exerts #"84 Pa"# of pressure and is at a temperature of #"320 K"#. If the pressure in the container changes to #"64 Pa"# with no change in the container's volume, what is the new temperature of the gas?

Using the ideal gas law to derive an equation is one method to accomplish this.

where

We can derive two ideal gas law relationships using this information:

Thus, we can divide these to obtain the new temperature:

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To find the new temperature of the gas, use Gay-Lussac's Law, which states that the pressure of a gas is directly proportional to its absolute temperature when the volume and the amount of gas are constant.

Given: Initial pressure, ( P_1 = 84 , \text{Pa} ) Initial temperature, ( T_1 = 320 , \text{K} ) Final pressure, ( P_2 = 64 , \text{Pa} )

Using Gay-Lussac's Law: ( \frac{P_1}{T_1} = \frac{P_2}{T_2} )

Substituting the given values: ( \frac{84}{320} = \frac{64}{T_2} )

Solving for ( T_2 ): ( T_2 = \frac{64 \times 320}{84} ) ( T_2 = \frac{20480}{84} ) ( T_2 \approx 244.76 , \text{K} )

Therefore, the new temperature of the gas is approximately 244.76 K.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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