A cup of coffee system mass 1 kg at 30 degree C rests on a t

A cup of coffee (system mass 1 kg) at 30 degree C rests on a table of height 1 m. An identical cup of coffee rests on the floor at a temperature of 25 degree C. Determine (a) the difference in the stored energy in the two systems, (b) what fraction of the difference can be attributed to potential energy? Use the Solid/Liquid (SL) volume state daemon. Assume properties of coffee to be similar to those of water.

Solution

Let’s find the energy possessed by the coffee in the cup placed on table.

Given details of Cup on table

Mass of coffee in cup m_t =1kg

Temperature of coffee = T_t = 30^oC = 303K

Height above the ground Z_t = 1m

Total Energy of Cup on table = Enthalpy of Coffee + potential energy      : (Neglecting other type of energies)

Enthalpy = m_t* Cp*T_t

Cp = specific heat of coffee assumed as water = 4180J/kg K

Potential Energy = m_t*g*Z_t

g = acceleration due to gravity = 9.81m/s

Total Energy of cup on table= (1*4180*303) + (1*9.81*1)= 1266549.81 J = 1266.54kJ

Now find the energy possessed by the coffee in the cup placed on ground.

Given details of Cup on ground

Mass of coffee in cup m_g =1kg

Temperature of coffee = T_g = 25^oC = 298K

Height above the ground Z_g = 0m

Total Energy of Cup on ground = Enthalpy of Coffee + potential energy      : (Neglecting other type of energies)

Enthalpy = m_g* Cp*T_g

Cp = specific heat of coffee assumed as water = 4180 J/kg K

Potential Energy = m_g*g*Z_g

g = acceleration due to gravity = 9.81m/s

Total Energy of cup on ground = (1*4180*298) + (1*9.81*0)= 1245640 J = 1245.64kJ

Difference in Stored energy = Total Energy of cup on Table - Total Energy of cup on ground

= 1266549.81 – 1245640 = 20909.81 J

Fraction of Difference attributed to Potential Energy = Potential energy possessed by Coffee cup on table/ Difference in Stored energy

                                                                         = (1*9.81*1)/20909.81

                                                                         = 0.000469