Question

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

(i) One mole of an ideal gas contained in a bulbof 10 litre capacity at 1 bar is allowed to enter into an evacuated bulb of 100 litre capacity.
(ii) One mole of a gas is allowed to expand from a volumeof 1 litre to a volume of 5 litres against the constant external pressure of 1 bar ( 1 litre bar = 100 J)
Calculate the internal energy change (ΔU) in each case if the process were carrid out adiabatically.

Answer 1

The work done by a gas expanding from 1 liter to 5 liters against an external pressure of 1 bar is -400 J. In an adiabatic process, this work is equal to the change in internal energy, ΔU, which is also -400 J.

Step-by-step explanation:

To calculate the work done by the expansion of a gas from a volume of 1 liter to 5 liters against an external pressure of 1 bar, we would use the formula W = -PΔV, where W is work, P is external pressure, and ΔV is the change in volume. The negative sign indicates work done by the system against the surroundings. Given that 1 liter bar = 100 J, we have:

W = - (1 bar) × (5 L - 1 L) = - (1 bar) × (4 L) = - (1 × 100 J/L × 4 L) = -400 J

Since the process is adiabatic, there is no heat transfer (Q = 0), and therefore according to the first law of thermodynamics, the change in internal energy ΔU is equal to the work done on the gas. Because the work was done by the gas, it will have lost that equivalent amount of internal energy, hence:

ΔU = -400 J

This is the change in internal energy for the adiabatic process described.