## 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.

Determine:

**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:*