The gas inside of a container exerts #32 Pa# of pressure and is at a temperature of #50 ^o K#. If the temperature of the gas changes to #80 ^oK# with no change in the container's volume, what is the new pressure of the gas?
The new pressure is
We apply Gay Lussac's Law
The final pressure is
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Use the ideal gas law: (P_1/T_1 = P_2/T_2). Solve for (P_2).
(P_2 = P_1 \times (T_2 / T_1))
(P_2 = 32 , Pa \times (80 , K / 50 , K))
(P_2 = 51.2 , Pa)
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To find the new pressure of the gas when the temperature changes, you can use the combined gas law, which states:
( P_1 \times V_1 / T_1 = P_2 \times V_2 / T_2 )
Where: ( P_1 ) = initial pressure ( V_1 ) = initial volume ( T_1 ) = initial temperature ( P_2 ) = final pressure (what we want to find) ( V_2 ) = final volume (which remains unchanged) ( T_2 ) = final temperature
Given: ( P_1 = 32 ) Pa ( T_1 = 50 ) K ( T_2 = 80 ) K ( V_1 = V_2 ) (volume remains unchanged)
Substitute the given values into the combined gas law equation and solve for ( P_2 ):
( P_1 \times V_1 / T_1 = P_2 \times V_2 / T_2 )
Since ( V_1 = V_2 ), we can cancel out the volumes:
( P_1 / T_1 = P_2 / T_2 )
Now, rearrange the equation to solve for ( P_2 ):
( P_2 = P_1 \times (T_2 / T_1) )
Substitute the given values:
( P_2 = 32 , \text{Pa} \times (80 , \text{K} / 50 , \text{K}) )
( P_2 = 32 , \text{Pa} \times 1.6 )
( P_2 = 51.2 , \text{Pa} )
Therefore, the new pressure of the gas when the temperature changes to ( 80 , ^\circ \text{K} ) with no change in volume is ( 51.2 , \text{Pa} ).
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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.
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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