Thermodynamics exercises

Internal Energy

1. What is the internal energy of 1.5 moles of a perfect gas at a temperature of 20 ° C? Conisdere R = 8.31 J / mol.K.

First you must convert the temperature of the Celsius scale to Kelvin:

From there just apply the data to the internal energy equation:

2. What is the internal energy of 3m³ of ideal gas under pressure of 0.5atm?

In this case we should use the internal energy equation together with the Clapeyron equation, like this:

Work of a gas

1. When 12 moles of a gas are placed in a piston container that maintains the pressure equal to the atmosphere, initially occupying 2m³. By pushing the plunger, the occupied volume becomes 1m³. Considering the atmospheric pressure of 100000N / m², what is the work done under the gas?

We know that the work of a perfect gas in an isobaric transformation is given by:

Substituting the values ​​in the equation:

The negative sign at work indicates that it is performed under gas and not by it.

2. A transformation is given by the chart below:

What work is done by this gas?

The work done by the gas is equal to the area under the graph curve, ie the area of ​​the blue trapezoid.

Being the trapezius area given by:

So, substituting the values ​​we have:

First Law of Thermodynamics

1. The graph below illustrates a 100 mol transformation of monoatomic ideal gas receives from the outside medium a heat quantity of 1800000 J. Given R = 8.31 J / mol.K.


The) the work done by the gas;

B) the variation of the internal energy of the gas;

ç) the gas temperature in state A.

The) The work done by the gas is given by the trapezius area under the graph curve, thus:

B) By the 1st law of thermodynamics we have that:

So, substituting the values ​​we have:

ç) By the Clapeyron equation:

Remembering that:

n = 100 moles

R = 8.31 J / mol.K

And by reading the graph:

p = 300000 N / m²

V = 1m³

Applying in the formula: