Question

the compressor exerts a pressure of 400 Pa to compress nitrogen gas from 3 L to 1 L. If no heat transfer occurs, how much will the internal energy of the gas change? (Note: 1 m3 = 1000 L.)

Answer 1

0.79014 J

Step-by-step explanation:

According to the first law of thermodynamics:-

`\Delta U = q + w`

Where,

U is the internal energy

q is the heat

w is the work done

From the question,

q = 0 J

The expression for the calculation of work done is shown below as:

`w=P* \Delta V`

Where, P is the pressure

`\Delta V` is the change in volume

From the question,

`\Delta V` = 3 - 1 L = 2 L

P = 400 Pa

The expression for the conversion of pressure in Pascal to pressure in atm is shown below:

P (Pa) =
`\frac {1}{101325}` P (atm)

Given the value of pressure = 43,836 Pa

So,

400 Pa =
`\frac {400}{101325}` atm

Pressure = 0.0039 atm

`w=0.0039* 2\ atmL`

Also, 1 atmL = 101.3 J

So,

`w=0.0039* 2* 101.3\ J=0.79014\ J` (work is done by the system)

So,

`\Delta U = 0\ J+0.79014\ J =0.79014\ J`