# Thread: Heat problems

1. ## Heat problems

1) Determine the amount of heat needed to turn 500g of ice in a 100g aluminum pan into steam.

2) What will be the phase of 1 liter of water in a 200g copper pot if it is placed in a coolant that absorbs 100,000J of heat?

3) How much heat is required to turn 50g of ice with temperature of -50 C to steam at 150 C?

Specific Heat:
Water = 4180 J/kg*K or 1.000 cal/g*C
Copper = 392 J/kg*K or 0.093 cal/g*C
Aluminum = 895 J/kg*K or 0.214 cal/g*C

Latent Heat:

= Heat of fusion
Water = $\displaystyle 3.34 * 10^5 J/kg$ or $\displaystyle 80 cal/g$
Copper = $\displaystyle 2.05 * 10^5 J/kg$ or $\displaystyle 48.9 cal/g$
Aluminum = $\displaystyle 3.76 * 10^5 J/kg$ or $\displaystyle 89.9 cal/g$

= Heat of vaporization
Water = $\displaystyle 22.6 * 10^5 J/kg$ or $\displaystyle 540 cal/g$
Copper = $\displaystyle 48 * 10^5 J/kg$ or $\displaystyle 1150 cal/g$
Aluminum = $\displaystyle 113.71 * 10^5 J/kg$ or $\displaystyle 2717.7 cal/g$

2. Originally Posted by ihmth
1) Determine the amount of heat needed to turn 500g of ice in a 100g aluminum pan into steam. My answer is 360,000 cal
If you are going to specify that we have an aluminum pan then we need to know what temperature the pan is starting at. Additionally we need to know what temperature the ice starts at as well. There is not enough information present to do this problem.

-Dan

3. Originally Posted by ihmth
2) What will be the phase of 1 liter of water in a 200g copper pot if it is placed in a coolant that absorbs 100,000J of heat? I dont have an answer

Specific Heat:
Water = 4180 J/kg*K or 1.000 cal/g*C
Copper = 392 J/kg*K or 0.093 cal/g*C

Latent Heat:

= Heat of fusion
Water = $\displaystyle 3.34 * 10^5 J/kg$ or $\displaystyle 80 cal/g$
The maximum amount of heat energy the water can have is when its initial temperature is at the boiling point, 373 K. (Otherwise it is steam, not water.) Assume the copper pot also has this temperature at the beginning.

Let's find out how much heat needs to be absorbed from the system to turn the water at the boiling point into ice:
$\displaystyle c_wm_w(373 - 273) + c_{Cu}m_{Cu}(373 - 273) + L_wm_w = 7.5984 \times 10^5~J$
(The copper pot must be a maximum of 273 K for the water to freeze, so I'm assuming that it drops at the same temperature rate as the water. This is not quite physically true, but will do as an approximation.) The first two terms take care of the heat needed to be absorbed to take the water and copper from 100 C to 0 C, the third term is the heat to be absorbed from the water at 0 C to turn it into ice.

The coolant absorbs $\displaystyle 1 \times 10^5~J$ of heat energy. This is less than the heat we can absorb from the water and copper at 100 C to freeze the ice, so we would need a starting temperature for the water-ice system in order to give a definitive answer to this question.

(Now if the coolant absorbed, say, $\displaystyle 1 \times 10^6~J$ then we would know for sure that the water would freeze.)

-Dan

4. Originally Posted by ihmth
3) How much heat is required to turn 50g of ice with temperature of -50 C to steam at 150 C? My answer is 41,000 cal

Specific Heat:
Water = 4180 J/kg*K or 1.000 cal/g*C

Latent Heat of fusion:
Water = $\displaystyle 3.34 * 10^5 J/kg$ or $\displaystyle 80 cal/g$

= Heat of vaporization
Water = $\displaystyle 22.6 * 10^5 J/kg$ or $\displaystyle 540 cal/g$
This one we can do:
Heat needed to turn the 50 g of ice at -50 C to ice at 0 C:
$\displaystyle c_im_i(0 - -50) = 5125~J$
($\displaystyle c_i = 2.050~J/g ^o C$. You didn't give this, I had to look it up. It's Wikipedia so I'm only assuming the numbers are correct.)

Heat needed to turn 50 g of ice at 0 C to water at 0 C:
$\displaystyle L_fm_i = 16700~J$

Heat needed to turn 50 g water at 0 C to water at 100 C:
$\displaystyle c_wm_w(100 - 0) = 20900~J$

Heat needed to turn 50 g water at 100 C to steam at 100 C:
$\displaystyle L_vm_w = 113000~J$

Finally, heat need to turn 50 g of steam at 100 C to steam at 150 C:
$\displaystyle c_sm_s(150 - 100) = 5200~J$
($\displaystyle c_s = 2.080~J/g ^oC$. Again, you didn't give us this information.)

Adding these up gives a total of 160925 J of heat required.

In the future, please provide us with all the information you are given.

-Dan

5. Originally Posted by topsquark
If you are going to specify that we have an aluminum pan then we need to know what temperature the pan is starting at. Additionally we need to know what temperature the ice starts at as well. There is not enough information present to do this problem.

-Dan
ice and the aluminum pan is at 0 C

6. Originally Posted by ihmth
ice and the aluminum pan is at 0 C
Originally Posted by ihmth
1) Determine the amount of heat needed to turn 500g of ice in a 100g aluminum pan into steam. My answer is 360,000 cal

Specific Heat:
Water = 4180 J/kg*K or 1.000 cal/g*C
Aluminum = 895 J/kg*K or 0.214 cal/g*C

Latent Heat:

= Heat of fusion
Water = $\displaystyle 3.34 * 10^5 J/kg$ or $\displaystyle 80 cal/g$

= Heat of vaporization
Water = $\displaystyle 22.6 * 10^5 J/kg$ or $\displaystyle 540 cal/g$
So
$\displaystyle L_f m_i + c_wm_i(100 - 0) + c_{Al}m_{Al}(100 - 0) + L_vm_i$

-Dan