Question

An ideal gas is compressed isothermally to one-third of its initial volume. The resulting pressure will be
a. three times as large as the initial value.
b. less than three times as large as the initial value.
c. more than three times as large as the initial value.
d. equal to the initial value.
e. impossible to predict on the basis of this data. 1

Answer 1

Answer: a. three times as large as the initial value.

Explanation:

To calculate the new pressure, we use the equation given by Boyle's law. This law states that pressure is inversely proportional to the volume of the gas at constant temperature (isothermal).  

The equation given by this law is:

$P_1V_1=P_2V_2$

where,

$P_1\text{ and }V_1$ are initial pressure and volume.

$P_2\text{ and }V_2$ are final pressure and volume.

We are given:

$P_1=p\\V_1=v\\P_2=?\\V_2=\frac{v}{3}$

Putting values in above equation, we get:

$p\times v=P_2\times \frac{v}{3}\\\\P_2=3p$

Thus the resulting pressure will be three times as large as the initial value.