Advertisements
Advertisements
प्रश्न
0.022 kg of CO2 is compressed isothermally and reversibly at 298 K from an initial pressure of 100 kPa when the work obtained is 1200 J, calculate the final pressure.
उत्तर
Given: Mass of CO2 = 0.022 kg = 22 g
Temperature = T = 298 K
Initial pressure = P1 = 100 kPa
Work done on system = Wmax = 1200 J
To find: Final pressure = P2
Formula: Wmax = – 2.303 nRT log10 `"P"_1/"P"_2`
Calculation: Number of moles of CO2 = n = `(22 "g")/(44 "g mol"^-1)` = 0.5 mol
Gas constant = R = 8.314 J K–1 mol–1
Now, using formula,
Wmax = – 2.303 nRT log10 `"P"_1/"P"_2`
1200 J = − 2.303 × 0.5 mol × 8.314 J K–1 mol–1 × 298 K × log10 `(100 "kPa")/"P"_2`
∴ `log_10 (100 "kPa")/"P"_2 = (- 1200)/(2.303 xx 0.5 xx 8.314 xx 298)`
Calculation using log table:
`(1200)/(2.303 xx 0.5 xx 8.314 xx 298)`
= Antilog10 [log10 1200 – (log10 2.303 + log10 0.5 + log10 8.314 + log10 298)]
= Antilog10 [3.0792 – (0.3623 + `bar"1"`.6990 + 0.9198 + 2.4742)]
= Antilog10 [3.0792 – (3.7563 + `bar"1"`.6990)]
= Antilog10 [`bar"1"`.6239] = 0.4207
= - 0.4207
∴ `(100 "kPa")/"P"_2` = antilog10 (– 0.4207) = 0.3796
∴ `"P"_2 = (100 "kPa")/0.3796`
= 263.4 kPa
The final pressure is 263.4 kPa.
APPEARS IN
संबंधित प्रश्न
Answer the following question.
Derive the expression for the maximum work.
Answer the following question.
Calculate the maximum work when 24 g of O2 are expanded isothermally and reversibly from the pressure of 1.6 bar to 1 bar at 298 K.
Write the expression to calculate maximum work done when 1 mole of an ideal gas expands isothermally and reversibly from V1 to V2.
An ideal gas expands from 1 × 10−3 m3 to 1 × 10−2 m3 at 300 K against a constant external pressure of 1 × 105 N m−2, work done is ____________.
What is the work done when 2 mole of an ideal gas is expanded isothermally and reversibly from 5 m3 to 10 m3 at 300 K? (R = 8.314 J K-1 mol-1)
One mole of an ideal gas is expanded isothermally and reversibly from 10 L to 15 L at 300 K. Calculate the work done in the process.
2000 mmol of an ideal gas expanded isothermally and reversibly from 20 L to 30 L at 300 K, calculate the work done in the process (R = 8.314 JK–1 mol–1).
Calculate work done when 0.5 moles of C02 is compressed isothermally and reversibly at 298 K from 100 kPa to 263.4 kPa. (R = 8.314 kJ mol-1 K-1)
Three moles of ideal gas is compressed isothermally and reversibly to a volume of 2 dm3 . The work done is 2.984 kJ at 22°c. Calculate V1 for the gas.
