Question

A. A cook leaves a plastic spoon and a wooden spoon in a pot of hot water for the same length of time. The spoons have the same mass. If plastic has a higher specific heat capacity than wood has, which spoon will have a smaller change in temperature? Write one or two sentences explaining your answer.
b. Does a closed system obey the law of conservation of energy? Write one or two sentences explaining your answer.

c. A hot piece of iron is placed into a container of water. Describe two ways in which heat is transferred in this system.

d. If 0.25 kg of iron at 100°C is added to 1.00 kg of water at 24.0°C, what is the final temperature of the system? Show your work.

e. To calculate the final temperature of the mixture, you had to assume that energy would not flow from the iron and water to the container. What type of system does this describe? Explain your answer.

f. If heat could flow to the container, how would the final temperature be affected?

Answer 1

a) The one with the higher capacity will have smaller change in temperature

b) Yes, because the total energy is saved (enclosed) inside.

c) Heat from hot iron heats the water, then if there is still enough heat, the water can boil and evaporate

d) Q2+Q1=0, Q1 is for Iron and Q2 is for water

-C1M1(t-T1)=C2M2(t-T2)

$t=\frac{C_1M_1T_1+C_2M_2T_2}{C_1M_1+C_2M_2}=26$ C.

e) Closed system (isolated system) because the energy is transferred only between water and iron.

f) It would be smaller.

Answer 2

A. The smallest change in temperature will be seen in the plastic spoon, as it has a higher specific heat capacity. Because of this, more heat is required per unit time in order to raise its temperature. The wood spoon will have a higher temperature.  

B. If it is a thermodynamic system, a closed system violates the law as it can exchange energy but not matter with its surroundings.  

C. Conduction – occurs through direct contact.

Within the iron piece, heat will move through conduction inside the iron piece towards the outside.. As the particles on the iron’s surface loose energy/heat to water, the higher energy/hotter particles in the core of the piece will, in turn, transfer energy to the surface particles. This is the first way of heat transfer. Through conduction, energy is also transferred from the iron atoms to the surrounding water atoms.  

Convection – occurs through the movement of a fluid (liquid or gas).  

As the iron looses heat to water, this heat will make the surrounding water hotter than the rest. Through convection, the water particles around the iron will gain energy and thus move faster and thus the liquid becomes less dense and rises. The cooler water will replace the warm water until it becomes less dense themselves. This process of heat transfer will continue as long as the iron is warmer than the water until an energy equilibrium is achieved.  

A hot piece of iron is placed into a container of water. Describe two ways in which heat is transferred in this system.

D. For an isolated system $m_{i}*c_{i}*(T_{f}-T_{i})+m_{w}*c_{w}*(T_{f}-T_{w})=0$.

As a result:

$T_{f} =\frac{m_{i}*c_{i}*T_{i}+m_{w}*c_{w}*T_{w}}{m_{i}*c_{i}+m_{w}*c_{w}\\ }$

$T_{f} =\frac{0,25*450*100+1*4180*24}{0,25*450+1*4180\\ }$

$T_{f} =26 C$

Where:

$m_{i}$ = mass of iron

$T_{i}$ = initial temperature of iron

$c_{i}$ = specific heat of iron = 450 J / (kg K) (- joules per kelvin)

$m_{w}$ = mass of water

$T_{w}$ = initial temperature of water

$c_{w}$ = specific heat of water = 4180 J / (kg K)

$T_{f}$ = final temperature

E. An isolated system as neither energy nor mass is transferred between the container and the water+iron system.

F. If heat could flow to the container, the final temperature would be lower, as energy will be absorbed by the container. In the end, all the components of the new system (iron+water+container) will reach an equilibrium and have the same temperature. The exact temperature will depend on the specific heat of the container itself.