please answer i detail, thank you. Water is contained in a cylinder fitted with

Question

please answer i detail, thank you.

Water is contained in a cylinder fitted with a piston containing stops Initially the piston is resting on the stops. The pressure cxerted on the water due to the weight of the piston and the atmospheric pressure is 30 psia Initially, the 5 Ibm of water is at 150 F with a quality of 0.60. Heat is added to the water until the water doubles in volume. Find a. Initial pressure of the water nitial volume of the water c. Amount of work done by the water d. Amount of heat added e. Sketch on a P-V diagram

Explanation / Answer

The above question is a case under Gas law.

Assuming temperature to be constant the problem needs to be solved as per Boyle's law

As per Boyles law " When temperature remains constant Volume is inversely proportion to Pressure

PV = k ( at constant temperature) where P=Pressure, V= Volume and K = constant

If Initial Pressure of Water P1, Initial Volume = V1, Final Pressure = P2 and Final Volume = V2.

Therefore as per Boyles law P1V1=k and P2V2=k, So PIVI = P2V2.

a. Initial Pressure = 30 psi

b. Initial Volume of water = P1V1= P2V2

P1V1 = P2. 2V1 (Since V2 = 2V1)

V1 = P2 x 2V1 / P1

V1/2V1 = P2/P1

P2/P1 = 1/2 (P2 =15 psi)

V1 =15 x 5 / 30 = 2.5

c. Amount of work done= P (V2-V1)

15 (5 - 2.5) = 15 x 2.5 = 37.5

d. Amount of heat added = Q = mst (where m = mass of water, s = pecific heat of water and t = Change in temperature)

Since temperature remains constant Q (heat) = 0

e. PV diagram

(e) PV graph

The P-V curve is a rectangular hyperbola with Volume along Y-axis and Pressure along X-Axis

It implies that when the pressure increases the Volume decreases. Hence the product PV of a given substance remains constant at constant temperature

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