# The gas inside of a container exerts #"24 Pa"# of pressure and is at a temperature of #"320 K"#. If the pressure in the container changes to #"32 Pa"# with no change in the container's volume, what is the new temperature of the gas?

The final temperature is 430 K.

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You can use the ideal gas law, ( PV = nRT ), where ( P ) is pressure, ( V ) is volume, ( n ) is the number of moles of gas, ( R ) is the gas constant, and ( T ) is temperature. Since the volume remains constant, we can simplify the equation to ( P_1/T_1 = P_2/T_2 ) where ( P_1 ) and ( T_1 ) are the initial pressure and temperature, and ( P_2 ) and ( T_2 ) are the final pressure and temperature.

Given that ( P_1 = 24 , \text{Pa} ), ( T_1 = 320 , \text{K} ), and ( P_2 = 32 , \text{Pa} ), we can rearrange the equation to solve for ( T_2 ):

[ T_2 = \frac{{P_2 \times T_1}}{{P_1}} ]

[ T_2 = \frac{{32 , \text{Pa} \times 320 , \text{K}}}{{24 , \text{Pa}}} ]

[ T_2 = 426.67 , \text{K} ]

So, the new temperature of the gas is ( 426.67 , \text{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.

- A container with a volume of #19 L# contains a gas with a temperature of #220^o C#. If the temperature of the gas changes to #320 ^o K# without any change in pressure, what must the container's new volume be?
- A container has a volume of #12 L# and holds #15 mol# of gas. If the container is expanded such that its new volume is #24 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?
- If #14/3 L# of a gas at room temperature exerts a pressure of #45 kPa# on its container, what pressure will the gas exert if the container's volume changes to #13/7 L#?
- A container has a volume of #3 L# and holds #2 mol# of gas. If the container is expanded such that its new volume is #12 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?
- If #8 L# of a gas at room temperature exerts a pressure of #42 kPa# on its container, what pressure will the gas exert if the container's volume changes to #9 L#?

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