Question
Class 11ChemistryThermodynamics

Calculate the amount of work done in each of following cases:-

(i) One mole of an ideal gas contained in a bulb of 10 litre capacity at 1 atm is allowed to enter into an evacuated bulb of 100 litre capacity. 

(ii) One mole of a gas is allowed to expand from a volume of 1 litre to a volume of 5 litre against the constant external pressure of 1 atm (1 litre atm = 101.3 J) 

Calculate the internal energy change (∆U) in each case if the process were carried out adiabatically. 

Verified Answer

Thermodynamics Calculations Conversion
(i) w = −Pext × ΔV
As expansion takes place into the evacuated bulb, i.e., against vacuum, Pext = 0. Hence, w = 0.
For adiabatic process, q = 0  ∴  ΔU = q + w = 0 + 0 = 0.
(ii) ΔV = V2 − V1 = 5 − 1 = 4 litres
P = 1 atm  ∴  w = −PΔV = −1 × 4 litre atm = −4 litre atm = −4 × 101.3 J = −405.2 J
Alternatively, using the SI units directly,
P = 1 atm = 101325 Pa ;      ΔV = 4 L = 4 × 10−3m3
∴ w = −P × ΔV = −101325 × 4 × 10−3 J = −405.3 J
The negative sign implies that the work is done by the system.
For adiabatic process, q = 0. Hence, ΔU = q + w = 0 − 405.2 J = −405.2J.