If both the pressure and volume of an ideal gas are increased, what will happen to the temperature, assuming the amount of gas remains constant?

• A. The temperature will decrease.
• B. The temperature will increase.
• C. The temperature will first increase, then decrease.
• D. The temperature will remain unchanged.

Answer: (B)

Verified step by step guidance

1. Recall the Ideal Gas Law, which relates pressure (P), volume (V), temperature (T), and amount of gas (n): \(P \times V = n \times R \times T\), where \(R\) is the ideal gas constant.
2. Since the amount of gas \(n\) remains constant, we can rearrange the equation to express temperature as \(T = \frac{P \times V}{n \times R}\).
3. If both pressure \(P\) and volume \(V\) increase, their product \(P \times V\) will increase as well, assuming the increases are positive.
4. Because \(n\) and \(R\) are constants, an increase in \(P \times V\) means that temperature \(T\) must increase to maintain the equality.
5. Therefore, when both pressure and volume increase for a fixed amount of gas, the temperature of the gas will increase.