Question

An ideal gas is confined within a closed cylinder at a pressure of 2.026 × 105 Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume. What is the final pressure of the gas when its temperature returns to its initial value?

Answer 1

Answer:

The final pressure of the gas when its temperature returns to its initial value $1.8234\times 10^6$ Pa.

Step-by-step explanation:

Given : An ideal gas is confined within a closed cylinder at a pressure of $2.026\times 10^5$ Pa by a piston. The piston moves until the volume of the gas is reduced to one-ninth of the initial volume.

To find : What is the final pressure of the gas when its temperature returns to its initial value?

Solution :

Since the temperature is constant .

The relation between P and V is given by,

$P_1\times V_1 = P_2\times V_2$

$\frac{P_1}{P_2}=\frac{V_2}{V_1}$ ....(1)

The piston moves until the volume of the gas is reduced to one-ninth of the initial volume i.e. $V_2=\frac{V_1}{9}$

or $\frac{V_2}{V_1}=\frac{1}{9}$

$P_1=2.026\times 10^5$

Substitute in equation (1),

$\frac{2.026\times 10^5}{P_2}=\frac{1}{9}$

$P_2=9\times 2.026\times 10^5$

$P_2=18.234\times 10^5$

$P_2=1.8234\times 10^6$

The final pressure of the gas when its temperature returns to its initial value $1.8234\times 10^6$ Pa.