A U-tube stands vertically and has fluid in it and the pressure on the left side

Question

A U-tube stands vertically and has fluid in it and the pressure on the left side on the surface of the fluid is P and the pressure on the other side is 3P . The acceleration of gravity is g . The density of the fluid is p . The cross sectional area of the tube is A . Calculate the difference in height of the two surfaces in terms of quantities given or a subset thereof. A chunk of hot copper of mass Mc = 100 grams is at a temperature 90 degrees Celsius when it is placed into a bucket of cold water at temperature 10 degrees Celsius. The water has mass Mw . The specific heat of water is 4.186 joule/gram degree C. The specific heat of copper is .386 joule/gram degree C . What is the final temperature of the system. Assume heat in the copper flows only into the water and the water is in an insulating bucket and does not lose energy.

Explanation / Answer

PROBLEM ONE (U-TUBE) : the forces on two sides should be equal. so

force due to pressure = pressure *(cross-section area)

equating the forces on two sides.

force due to gravity = mass * gravity(g)

mass = density(rho) * volume

volume = Area of cross-section * height

height difference in U-tubes = h

3P*A = P*A + (rho) * (A*h) *g

2PA = h *(rho*Ag)

h = 2PA /(rho*Ag)

PROBLEM ONE (heat transfer):Q = ms (t)

(Q = ms Delta t)

where m = mass ,s = specific heat, (Delta t = difference in temperatue(temp. change))

the total heat transfer will stop when the whole system get a uniform temp. let that temp be T

the heat loss of copper = heat gain of water.

(laws of thermodynamics)

Mc * s * (90 -T) = Mw *s *(T -10)

100 * 0.386 *(90-T)= Mw * 4.186 * (T-10)

solve for T.

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