Answer to Question #249206 in Mechanical Engineering for russman

Question

A quantity of gas has an initial pressure of 140 kN/m² and volume 0.14 m³ It then compressed to a pressure of 700 kN/m² while the temperature remains constant Determine the final volume of the gas.

Answer 1

Q249206

A quantity of gas has an initial pressure of 140 kN/m² and a volume of 0.14 m³. It is then compressed to a pressure of 700 kN/m² while the temperature remains constant Determine the final volume of the gas.

Solution :

In the question, both the pressures are given in the same units. There would be no need to convert the pressure to another unit. Only when using the Ideal gas equation PV = n RT you will have to pay attention to the units.

We are given the initial pressure and volume of the gas. The temperature is kept constant and the gas is compressed by increasing the pressure to 700 kN/m². We have to find the final volume after increasing the pressure of the gas to 700 kN/m².

Boyle's law is the one that relates the volume and pressure of the gas at a constant temperature.

For two different sets of conditions, Boyle's law can be written as

$$P_1 \ V_1 = P_2 \ V_2$$

The information given to us is

P₁ = 140 kN/ m²

V₁ = 0.14 m³

P₂ = 700 kN/m²

V₂ = unknown

plug all this information in the formula we have

$$\frac{140 \ kN/m^2 \ * 0.14 \ m^2 }{ 700 \ kN/m^2} = \frac{ 700 \ kN/m^2 \ * \ V_2 }{700 \ kN/m^2}$$

dividing both the side by 700 kN/m², we have

$$\frac{140 \ kN/m^2 \ * 0.14 \ m^2 }{ 700 \ kN/m^2} = \frac{ \cancel{700 \ kN/m^2} \ * \ V_2 }{\cancel{700 \ kN/m^2}}$$

$$\frac{140 \ \cancel{kN/m^2 } \ * 0.14 \ m^2 }{ 700 \ \cancel{kN/m^2 }} = V_2$$

$$\frac{140 * 0.14 \ m^2 }{ 700 } = V_2$$

$$V_2 = \frac{19.6 \ m^2 }{700} = 0.028 \ m^2.$$

In the question, we are given 700 kN/m²  in 1 significant figure, so our final answer must also be in 1 significant figure.

In the correct significant figure, the answer is 0.03 m³.

Hence the final volume of the gas would be 0.03 m³.