A gas within a piston-cylinder assembly undergoes compression at constant temperature. According to the ideal gas law, what happens to the pressure of the gas?

• A. The pressure remains constant as the volume decreases.
• B. The pressure increases as the volume decreases.
• C. The pressure decreases as the volume decreases.
• D. The pressure first increases, then decreases as the volume decreases.

Answer: (B)

Verified step by step guidance

1. Recall the ideal gas law, which is given by the equation \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles of gas, \(R\) is the ideal gas constant, and \(T\) is temperature.
2. Since the problem states that the temperature is constant, and assuming the amount of gas \(n\) is also constant, the product \(P \times V\) must remain constant (this is known as Boyle's Law).
3. This means that pressure and volume are inversely proportional: if volume decreases, pressure must increase to keep the product \(P \times V\) constant.
4. Therefore, as the gas is compressed (volume decreases) at constant temperature, the pressure of the gas increases.
5. This relationship can be summarized mathematically as \(P_1 \times V_1 = P_2 \times V_2\), where the subscripts 1 and 2 refer to initial and final states respectively.