If the pressure of the gas increases in a container held at a constant volume, what is the most likely outcome for the temperature?

Question

A. The temperature will rise at the same rate with the increase in pressure.
B. The temperature will decline proportionally to the rate of pressure increase.
C. The temperature will rise at half the rate of the pressure increase.
D. The temperature will drop at half the rate of the pressure increase.

Answer 1

According to the Ideal Gas Law, which states that \( PV = nRT \) (where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles of gas, \( R \) is the gas constant, and \( T \) is temperature), if the volume of the container is held constant and the amount of gas does not change, an increase in pressure will result in a corresponding increase in temperature.

Since pressure and temperature are directly proportional when the volume remains constant (as given by the rearranged form \( T = \frac{PV}{nR} \)), if pressure increases, temperature must also increase to maintain the equality.

Therefore, the most likely outcome for the temperature is:

A. The temperature will rise at the same rate with the increase in pressure.