How Does Temperature Affect Density and Pressure in Thermodynamics?

[Ne0]

All physics problems come from the Resnick and Halliday Physics text 5th edition, volume 1, Chapter 21-22.

E21-25:
Density is mass divided by volume. If the volume V is temperature dependent, so is the density (row). Show that the change in density (delta row) with change in temperature (delta T) is given by: (delta row) = - (Beta)*(row)*(delta T) where (Beta) is the coefficient of volume expansion. Explain the minus sign.

P21-3:
Show that when the temperature of a liquid in a barometer changes by (delta T), and the pressure is constant, the height h changes by (delta h) = (Beta)*(h)*(delta T), where (Beta) is the coefficient of volume expansion of the liquid. Neglect the expansion of the glass tube.

P21-10:
Consider a mercury-in-glass thermometer. Assume that the cross section of the capillary is constant at A and that V is the volume of the bulb of mercury at 0.00 degrees celsius. Suppose that the mercury just fills the bulb at 0.00 degrees celsius. Show that the length L of the mercury column in the capillary at a temperature T, in degrees celsius, is
L = (V/A)*((Beta)-3*(alpha))*T, that is proportional to the temperature, where (Beta) is the coefficient of volume expansion of mercury and (alpha) is the coefficient of linear expansion of glass.

P22-2:
Dalton's Law states that when two mixtures of gases having no chemical interaction are present together in a vessel, the pressure exerted by each constituent at a given temperature is the same as it would exert if it alone filled the vessel, and that the total pressure is equal to the sum of the partial pressures of each gas. Derive this law from kinetic theory using
P = (1/3)*(row)*(v^2).

All and any help is greatly appreciated and thanks in advance. If I could atleast get a hint towards the correct direction to solve these problems that would be very helpful. Thanks again,
Ron Foxall

 

[siddharth]

Ne0, if you read the https://www.physicsforums.com/showthread.php?t=5374", you will see that you need to show your work before you get help

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