Answer to Question #249210 in Mechanical Engineering for russman

Question

A mass of gas has an initial pressure of 1 bar and a temperature of 20 ⁰C. The temperature of the gas is now increased to 550 ⁰C while the volume remains constant. Determine the final pressure of the gas.

Answer 1

Q249210

A mass of gas has an initial pressure of 1 bar and a temperature of 20 ⁰C. The temperature of the gas is now increased to 550 ⁰C while the volume remains constant. Determine the final pressure of the gas.

Solution :

The initial pressure and temperature of the gas are 1 bar and 20 ^oC respectively.

Here volume is kept constant and the temperature is increased to 550 ⁰C.

We can use the law which relates the pressure and temperature and keeping all other things like moles, and volume constant.

Amonton's law relates pressure and temperature at constant volume.

For two different sets of conditions, the law can be written as

$$\frac{P_1}{T1} = \frac{P_2}{T_2}$$

In the question, we are given the temperatures in degrees celsius, we will have to convert it to Kelvin.

P₁ = 1 bar,

T₁ = 20 ⁰C = 20 + 273.15 = 293.15 K

P₂ = unknown,

T₂ = 550 ⁰C = 550 + 273.15 = 823.15 K

plug all this information in the formula we have

$$\frac{1 \ bar }{293.15 \ K } = \frac{P_2}{823.15 \ K }$$

Arranging this equation for P₂, we have

$$\frac{1 \ bar }{293.15 \ K } * 823.15 \ K = P_2$$

$$2.8079 \ bar = P_2$$

In the correct significant figure, the answer is 3 bar.

Hence the final pressure of the gas will be 3 bar.