Alright, let's solve this step-by-step using the Ideal Gas Law, which is expressed as [tex]\( PV = nRT \)[/tex].
Here's what the Ideal Gas Law equation represents:
- [tex]\( P \)[/tex] is the pressure of the gas.
- [tex]\( V \)[/tex] is the volume of the gas.
- [tex]\( n \)[/tex] is the amount of gas (in moles).
- [tex]\( R \)[/tex] is the universal gas constant.
- [tex]\( T \)[/tex] is the absolute temperature of the gas.
Initially, we have the equation:
[tex]\[ P_1 \cdot V_1 = n \cdot R \cdot T_1 \][/tex]
Let's examine what happens when the volume and temperature are both doubled:
- New volume ([tex]\( V_2 \)[/tex]) is [tex]\( 2 \cdot V_1 \)[/tex]
- New temperature ([tex]\( T_2 \)[/tex]) is [tex]\( 2 \cdot T_1 \)[/tex]
Thus, the new equation becomes:
[tex]\[ P_2 \cdot (2 \cdot V_1) = n \cdot R \cdot (2 \cdot T_1) \][/tex]
Next, divide both sides by 2:
[tex]\[ P_2 \cdot V_1 = n \cdot R \cdot T_1 \][/tex]
Notice that this resulting equation is identical to our initial equation:
[tex]\[ P_1 \cdot V_1 = n \cdot R \cdot T_1 \][/tex]
This demonstrates that:
[tex]\[ P_2 = P_1 \][/tex]
Therefore, the pressure of the gas has stayed the same.
The correct answer is:
- It has stayed the same.
