Question

If I have 5.1 m3 of gas in a piston at a pressure of 87 kPa and compress the gas until its volume is 2.8 m3, what will the new pressure inside the piston be? Temperature is constant.

Answer 1

Answer: The new pressure will be 158.46 kPa

Step-by-step 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.

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=87kPa\\V_1=5.1m^3\\P_2=?kPa\\V_2=2.8m^3`

Putting values in above equation, we get:

`87kPa* 5.1m^3=P_2* 2.8m^3\\\\P_2=158.46kPa`

Hence, the new pressure will be 158.46 kPa

Answer 2

158.4643 kPa

Step-by-step explanation:

Using Boyle's law

`{P_1}* {V_1}={P_2}* {V_2}`

Given ,

V₁ = 5.1 m³

V₂ = 2.8 m³

P₁ = 87 kPa

P₂ = ?

Using above equation as:

`{P_1}* {V_1}={P_2}* {V_2}`

`{87}* {5.1}={P_2}* {2.8}`

`{P_2}=\frac {{87}* {5.1}}{2.8}\ kPa`

`{P_2}=158.4643\ kPa`

The new pressure of the gas is 158.4643 kPa.