Two moles of an ideal gas initially at 27C and 1 atm pressure are compressed isothermally and reversibly till the final pressure of the gas is 10 atm. Calculate the work done. (R=8.314 JK-1mol-1)
w = nRTln(V2/V1)
and since work is being done on the gas the sign of w is +.
To calculate the work done during an isothermal and reversible compression of an ideal gas, we can use the formula:
Work = -nRT ln(Vf/Vi)
Where:
- Work is the work done on/by the gas during the compression (in Joules)
- n is the number of moles of gas (in this case, n = 2 moles)
- R is the ideal gas constant (R = 8.314 J K^(-1) mol^(-1))
- T is the temperature of the gas in Kelvin (T = 27°C + 273.15 = 300.15 K)
- Vi is the initial volume of the gas
- Vf is the final volume of the gas
Since the initial and final pressures are given, and the process is isothermal, we can use the ideal gas law to relate the initial and final volumes:
P1V1 = P2V2
Where:
- P1 is the initial pressure (P1 = 1 atm)
- V1 is the initial volume (unknown)
- P2 is the final pressure (P2 = 10 atm)
- V2 is the final volume (unknown)
Rearranging the equation, we get:
V1 = (P2/P1) * V2
Now, substituting this value of V1 into the formula for work:
Work = -2 * (8.314 J K^(-1) mol^(-1)) * (300.15 K) * ln((10 atm / 1 atm) * V2/V2)
Simplifying further:
Work = -2 * (8.314 J K^(-1) mol^(-1)) * (300.15 K) * ln(10)
Finally, you can calculate the numerical value of work using a calculator.