What is the additional pressure required to decrease the volume of a gas from 2.5 L to 1.5 L at constant temperature?
Understand the Problem
The question is asking for the calculation of additional pressure needed to reduce the volume of a gas while keeping the temperature constant. This involves using principles from gas laws, specifically Boyle's Law.
Answer
The additional pressure needed is calculated as $P_2 - P_1$.
Answer for screen readers
The additional pressure needed is given by the equation:
$$ \text{Additional Pressure} = P_2 - P_1 $$
Steps to Solve
- Recall Boyle's Law
Boyle's Law states that at constant temperature, the pressure of a gas is inversely proportional to its volume. This can be represented mathematically as:
$$ P_1V_1 = P_2V_2 $$
Where ( P_1 ) is the initial pressure, ( V_1 ) is the initial volume, ( P_2 ) is the final pressure, and ( V_2 ) is the final volume.
- Identify known values
Identify the values provided in the problem. Let's say we have ( P_1 ), ( V_1 ), and ( V_2 ). You may need to read these values from the problem statement.
- Rearrange the equation for ( P_2 )
To find the final pressure ( P_2 ), rearrange the equation:
$$ P_2 = \frac{P_1V_1}{V_2} $$
This shows how pressure changes in response to changes in volume while keeping the temperature constant.
- Calculate ( P_2 )
Now, substitute your known values for ( P_1 ), ( V_1 ), and ( V_2 ) into the equation:
$$ P_2 = \frac{(P_1) \times (V_1)}{(V_2)} $$
- Determine the additional pressure needed
To find the additional pressure required, calculate the difference between ( P_2 ) and ( P_1 ):
$$ \text{Additional Pressure} = P_2 - P_1 $$
This step gives you the additional pressure needed to reduce the volume of the gas.
The additional pressure needed is given by the equation:
$$ \text{Additional Pressure} = P_2 - P_1 $$
More Information
The result illustrates how gases behave under varying pressure and volume while adhering to Boyle's Law, important for understanding concepts in thermodynamics and physics.
Tips
- Confusing volume and pressure values, leading to incorrect calculations. Make sure to carefully identify ( P_1 ), ( V_1 ), and ( V_2 ).
- Forgetting to keep temperature constant, which is crucial for applying Boyle's Law correctly.
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