Physics : Heat and Thermodynamics - Solved Example Problems for Isothermal process, Solved Example Problems for Thermodynamic Processes

A 0.5 mole of gas at temperature 300 K expands isothermally from an initial volume of 2 L to 6 L

(a) What is the work done by the gas?

(b) Estimate the heat added to the gas?

(c) What is the final pressure of the gas? (The value of gas constant, R = 8.31 J mol-1 K-1)

(a) We know that work done by the gas in an isothermal expansion

Since Âµ = 0.5

*W *= 1.369* kJ*

Note that W is positive since the work is done by the gas.

(b) From the First law of thermodynamics, in an isothermal process the heat supplied is spent to do work.

Therefore, *Q* = *W* = 1.369 *kJ*. Thus Q is also positive which implies that heat flows in to the system.

(c) For an isothermal process

*P*i*V*i* *=* P*fVf* *= Âµ*RT*

=207.75 *k Pa*

The following PV curve shows two isothermal processes for two different temperatures and. Identify the higher temperature of these two.

To determine the curve corresponding to higher temperature, draw a horizontal line parallel to x axis as shown in the figure. This is the constant pressure line. The volumes *V*1 and *V*2 belong to same pressure as the vertical lines from *V*1 and *V*2 meet the constant pressure line.

At constant pressure, higher the volume of the gas, higher will be the temperature. From the figure, as *V*1 > *V*2 we conclude *T*1* *>* T*2. In general the isothermal curve* *closer to the origin, has lower temperature.

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11th Physics : UNIT 8 : Heat and Thermodynamics : Solved Example Problems for Isothermal process |

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