Question

As the pressure of a gas decreases to half its original value, what happens to the volume of the gas if temperature is held constant?
A. The volume decreases to one-fourth of its original value
B. The volume decreases to half of its original value
C. The volume increases to twice its original value
D. The volume increases to four times its original value

Answer 1

According to Boyle's Law, which states that the pressure of a given mass of gas is inversely proportional to its volume when temperature is held constant, we can express this as:

\[ P_1 \times V_1 = P_2 \times V_2 \]

Given that the pressure (\( P \)) decreases to half its original value (\( P_2 = \frac{1}{2}P_1 \)), we can plug this into the equation.

Let’s denote the original volume as \( V_1 \) and the new volume as \( V_2 \):

\[ P_1 \times V_1 = \left(\frac{1}{2} P_1\right) \times V_2 \]

Now, we can simplify this equation:

\[ V_2 = 2 \times V_1 \]

This means that when the pressure is decreased to half of its original value while keeping the temperature constant, the volume of the gas increases to twice its original value.

Thus, the answer is **C. The volume increases to twice its original value**.