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

Answer:

0.79014 J

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:

$w=P\times \Delta V$

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

$w=0.0039\times 2\ atmL$

Also, 1 atmL = 101.3 J

So,  

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

So,

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