In this problem, we will consider an isothermal expansion of an ideal gas. Since

Question

In this problem, we will consider an isothermal expansion of an ideal gas. Since the gas expands, its volume increases and it does work. We will need to use the equation, W=nRTlnV2V1, for the work done by a gas that expands at a constant temperature. (Figure 1) shows a slow, controlled isothermal expansion of 3.0 moles of an ideal gas. The initial volume of the gas is 4.0 L and the final volume is 5.0 L. While the gas expands, heat is supplied from a flame to maintain the temperature at 300 K. How much work does the gas do during the expansion? What is the change in the internal energy of the gas?

SOLUTION

SET UP AND SOLVE From the equation in the introduction,

W===nRTln(V2V1)(3.0mol)[8.314J/(mol?K)](300K)ln(5.0L4.0L)1700J

Because the temperature is constant and the substance is an ideal gas, the change in internal energy is zero.

REFLECT Because the internal energy does not change, all of the heat entering the system goes into work.

Part A - Practice Problem:

If 2200 J of heat is added isothermally to 3.5 moles of an ideal gas with an initial volume of 3.0 L and a constant temperature of 300 K, what is the final volume of the gas?

Express your answers in liters to two significant figures.

In this problem, we will consider an isothermal expansion of an ideal gas. Since the gas expands, its volume increases and it does work. We will need to use the equation, W=nRTlnV2V1, for the work done by a gas that expands at a constant temperature. (Figure 1) shows a slow, controlled isothermal expansion of 3.0 moles of an ideal gas. The initial volume of the gas is 4.0 L and the final volume is 5.0 L. While the gas expands, heat is supplied from a flame to maintain the temperature at 300 K. How much work does the gas do during the expansion? What is the change in the internal energy of the gas?

SOLUTION

SET UP AND SOLVE From the equation in the introduction,

W===nRTln(V2V1)(3.0mol)[8.314J/(mol?K)](300K)ln(5.0L4.0L)1700J

Because the temperature is constant and the substance is an ideal gas, the change in internal energy is zero.

REFLECT Because the internal energy does not change, all of the heat entering the system goes into work.

Part A - Practice Problem:

If 2200 J of heat is added isothermally to 3.5 moles of an ideal gas with an initial volume of 3.0 L and a constant temperature of 300 K, what is the final volume of the gas?

Express your answers in liters to two significant figures.

Explanation / Answer

in isothetmal process total energy given to the system will be used as work done by system.

so w =nRTln(v2/v1)

2200 = 3.5×8.314×300×ln(v2/3)

ln(v2/3) = 2200/(3.5×8.314×300)

v2 = 3.86 liter

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