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The volume of a fixed amount of gas is doubled, and the absolute temperature is doublec
how has the pressure of the gas changed?
O It has increased to two times its original value.
O It has increased to four times its original value.
It has decreased to one-half its original value.
It has stayed the same.

Verified Answer :

GinnyAnswer

Alright, let's solve this step-by-step using the Ideal Gas Law, which is expressed as \(\( PV = nRT \)\).

Here's what the Ideal Gas Law equation represents:
- \(\( P \)\) is the pressure of the gas.
- \(\( V \)\) is the volume of the gas.
- \(\( n \)\) is the amount of gas (in moles).
- \(\( R \)\) is the universal gas constant.
- \(\( T \)\) is the absolute temperature of the gas.

Initially, we have the equation:
\(\[ P_1 \cdot V_1 = n \cdot R \cdot T_1 \]\)

Let's examine what happens when the volume and temperature are both doubled:
- New volume (\(\( V_2 \)\)) is \(\( 2 \cdot V_1 \)\)
- New temperature (\(\( T_2 \)\)) is \(\( 2 \cdot T_1 \)\)

Thus, the new equation becomes:
\(\[ P_2 \cdot (2 \cdot V_1) = n \cdot R \cdot (2 \cdot T_1) \]\)

Next, divide both sides by 2:
\(\[ P_2 \cdot V_1 = n \cdot R \cdot T_1 \]\)

Notice that this resulting equation is identical to our initial equation:
\(\[ P_1 \cdot V_1 = n \cdot R \cdot T_1 \]\)

This demonstrates that:
\(\[ P_2 = P_1 \]\)

Therefore, the pressure of the gas has stayed the same.

The correct answer is:
- It has stayed the same.

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