# A system of monoatomic ideal gas at pressure p=3x10^5 Pa and initial temperature of T = 300K slowly expands at constant pressure from a volume of 0.5m^3 to 0.6 m^3. Let the gas constant be R=8.314...

A system of monoatomic ideal gas at pressure p=3x10^5 Pa and initial temperature of T = 300K slowly expands at constant pressure from a volume of 0.5m^3 to 0.6 m^3. Let the gas constant be R=8.314 J/mol. K.

Find the work done by the gas on environment.

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### 1 Answer

Initially, the pressure was 3x10^5 Pa, temperature, 300K and volume, 0.5m^3.

Putting these values in the gas equation, PV=nRT

we get, n = PV/RT = 3*10^5*0.5/(8.314*300)=60.14 moles.

The ideal gas expands slowly under constant pressure and temperature. Hence the expansion is a reversible isothermal expansion.

Work done in this process `=nRTln(V_f/V_i) `

= `60.14*8.314*300ln(0.6/0.5)`

= `27.35 kJ` .

**Therefore, the work done by the gas on environment is 27.35 kJ**.

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