Question

An ideal gas is compressed isothermally and reversibly at 400K from 1 m3 to 0.5 m3 9200 J heat is evolved during compression. What is the work done and how many moles of gas were compressed during this process?

Answer 1

Answer : The work done on the system is 9200 J and the number of moles of gas is 3.99 moles.

Explanation : Given,

Initial volume of gas =
`1m^3`

Final volume of the gas =
`0.5m^3`

Temperature of the gas = 400 K

Heat evolved = -9200 J

According to the question, this is the case of isothermal reversible compression of gas.

As per first law of thermodynamic,

`\Delta U=q+w`

where,

`\Delta U` = internal energy

q = heat

w = work done

As we know that, the term internal energy is the depend on the temperature and the process is isothermal that means at constant temperature.

So, at constant temperature the internal energy is equal to zero.

`q=-w`

Thus, the work done on the system = -q = -(-9200J) = 9200 J

The expression used for work done will be,

`w=-nRT\ln ((V_2)/(V_1))`

where,

w = work done on the system = 9200 J

n = number of moles of gas = ?

R = gas constant = 8.314 J/mole K

T = temperature of gas = 400 K

`V_1` = initial volume of gas =
`1m^3`

`V_2` = final volume of gas =
`0.5m^3`

Now put all the given values in the above formula, we get the number of moles of gas.

`9200J=-n* 8.314J/moleK* 400K* \ln ((0.5m^3)/(1m^3))`

`n=3.99mole`

Therefore, the work done on the system is 9200 J and the number of moles of gas is 3.99 moles.