Question

(b) How much ice remains when the system reaches equilibrium? 106.16 9 Need Help? Eien■ 9 20 P027 One mole of an ideal gas is heated slowly so that it goes from the PV state (P, V,) to (68, 6V) in such a way that the pressure is directly proportional to the volume. (a) How much work is done on the gas in the process? (Use any variable or symbol stated above along with the following as necessary: in and (b) How is the temperature of the gas related to its volume during this the following as necessary: n, R, V, Vi, and Pi)

Answer 1

Solution :- first draw a diagram of this process; that is, a pVdiagram. You can see that the diagram will just be a diagonal linefrom (V, p) to (6V, 6p)

Work done is the area between this line and the V axis.This consists of a rectangle of height p and width 6V - V = 5V      or     area = 5 pV

and a triangle of height 6p - p = 5p and width 6V - V = 5V

or    area   = (1/2) x 5p x 5V = (25/2) pV

So the work done BY the gas is 5 pV + (25/2) pV = 17.5 pV

The work done ON thegas is = - 17.5 pV

Using the ideal gas law, pV = nRT , we can see that temp is proportional to the product pV. But Since p is proportional to V, then

T = (P_i / nRV_i​) V²