Question

a gas is present at a pressure of 2 atm .what should be the increase in pressure so that the volume of the gas can be decreased to 1/4th of the initial value if the temperature is maintained constant?

Answer 1

The increase in pressure is $\frac{1}{4}$ so that the volume of the gas can be decreased to 1/4th of the initial value if the temperature is maintained constant

Explanation:

To calculate the increase in pressure, we use the equation given by Boyle's law. This law states that pressure is directly proportional to the volume of the gas at constant temperature.  

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:

$P_1=2atm\\V_1=1mL\\P_2=?\\V_2=\frac{1}{4}mL$

Putting values in above equation, we get:

$2\times 1=P_2\times\frac{1}{4}\\P_2=8atm$

Thus the increase in pressure is $\frac{1}{4}$

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