Question

"A monatomic ideal gas is compressed isothermically to one-third of its initial volume. The resulting pressure will be ________________.

A) less than three times as large as the initial value.
B) equal to the initial value.
C) three times as large as the initial value.
D) more than three times as large as the initial value.
E) impossible to predict on the basis of this data"

Answer 1

The resulting pressure of a monatomic ideal gas when it is compressed isothermally to one-third of its initial volume will be three times as large as the initial value.

Step-by-step explanation:

The question is asking about the behavior of a monatomic ideal gas during an isothermal compression. When a monatomic ideal gas is compressed isothermally (meaning the temperature remains constant) to one-third of its initial volume, Boyle's Law applies, which states that the pressure of a given mass of an ideal gas is inversely proportional to its volume when the temperature is kept constant (P1V1 = P2V2). Thus, if the volume is reduced to one-third, the pressure will increase to three times its initial value, since P1V1 = P2V2 implies (P1)(V1) = (P2)(1/3V1), and hence P2 = 3P1.