2 and 3 A gas within a piston expands from 0.255 L to 0.892 L against a constant

Question

2 and 3

A gas within a piston expands from 0.255 L to 0.892 L against a constant external pressure of 0.987 atm, In this process, the piston cools from 23.5 degree C to 22.6 degree C. What is the total change the internal energy for the system? Assume the specific heat capacity of the piston is 0.88 J/g, degree C and it has a mass of 1.25 kg. Real gasses do not behave exactly as the ideal gas las would predict. One attempt to correct this is the Van Der Waals equation of state : The ideal gas law neglects intermolecular forces and the volume of a gas. The constant a corrects for the attraction between two molecules and the constant b takes into account the volume of a molecule. Calculate the work done during the reversible isothermal expansion of 3.7 moles of ammonia from 81 L to 170 L at 300. K. for ammonia, a = 4.225 l^2 bar mol^-1 and b = 0.0371L/mol

Explanation / Answer

(2)

We know that,

Change in internal energy = q + w ----------- (1)

w = p (V2 - V1)

w = 0.987 * ( 0.892 - 0.255)

w = 0.629 atm.L

w = 0.629 * 101.325 J

w = 63.7 J

And

q = m * s ( t2 - t1)

q = 1.25 * 1000 * 0.88 * (22.6 - 23.5)

q = - 990 J

From (1)

change in internal energy = - 990 - 63.7 = - 1053.7 J

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