plz help im crying

Question

n a factory, various metal pieces are forged and then plunged into a cool liquid to quickly cool the metal. Assume you have a cadmium rod, with a specific heat of 0.231 joules per gram degrees Celsius [J / (g °C)]. The metal pieces vary in mass, and are produced at a temperature of 572 degrees Fahrenheit [°F]. The ideal process lowers the temperature of the material to 122 degrees Fahrenheit [°F]. The liquid used to cool

the metal is glycerol. At the end of the process, the glycerol and the metal will be at the same temperature. The properties of glycerol are listed below.

Material Property Specific heat Specific gravity Initial temperature

Value [Units] 2400 J/(kg K) 1.261

20°C

Determine the volume of fluid, in units of gallons [gal], needed to cool a 6.5-kilogram [kg] rod of cadmium.

Answer 1

STEP 1: INTERPRET AND RE-WRITE THE PROBLEM:

Read the problem a few times until you agree with what I have interpreted the problem to mean (below). A 6.5Kg Cadmium rod is plunged into a liquid (glycerol) which is held at an initial temperature of 20°C in order to cool it from 572°F to 122°F.

You are given additional information about both Cadmium and Glycerol.

Specific Heat of Cd = 0.231 J/gm-C

Specific Heat of Glycerol = 2400 J/Kg-K

Specific Gravity of Glycerol = 1.261

You are asked to calculate the volume of glycerol needed to cool the rod.

STEP 2: MAKE ALL UNITS CONSISTENT.

Usually the volume is stated in MKS units, so, it is best to convert all quantities to MKS system.

STEP 3: WRITE THE ENERGY BALANCE EQUATION:

When the rod is immersed in glycerol, the rod loses temperature (and therefore, heat energy). Loss of energy is given by

ΔE_Rod = M_Rod * C_Rod * ΔT_Rod

On the other hand, glycerol liquid absorbs heat from the rod and gets hotter. It gains energy. That energy is written simply as

ΔE_Gly = M_Gly * C_Gly * ΔT_Gly

M_Gly = V_Gly/ρ, where ρ is the density of glycerol.

Note there is a difference between density ρ and specific gravity. The latter is a relative value of density compared to that of a standard (water at 4ºC). It is a dimensionless constant. Since the reference density of water has a value equal to 1, the numerical values of density and specific gravity are equal. So, we can use the value given for specific gravity, but with units of density.

Conservation of Energy principle requires that the energy lost by Cd rod must equal energy gained by glycerol. Therefore,

ΔE_Rod = ΔE_Gly

Using this equality, you should be able to solve the problem...without sweat and tear :)

Answer 2

What is happening in the problem? Start by writing, in math language, what you know. I will not work this out for you. That will not help you learn. I will guide you through the problem. Contact me on the site. Do not worry about money.