Specific and Latent Heats ---------------------------- Joseph F. Alward, PhD Department of  Physics   University of the Pacific

 

Heat Unit: One "calorie" (cal) = 4.186 Joules

   Specific Heat Capacity

Specific heat capacity, c:   The amount of heat per gram which must be gained or lost to raise or lower the temperature 1 C. Penny, marble, aluminum are at the same temperature. Which one stays hot longer after removal from the bath?

   Specific Heat Capacity

DT  = Q/mc --------------------------------- Same heat is absorbed. Iron's ability to store heat is less than water's. Iron's temperature rises more than does the water's.

  Specific Heat Capacity
   Q = mc DT

Substance	Specific Heat (cal/g-C)
Water	1.00
Aluminum	0.215
Iron	0.108
Gold	0.031

  Specific Heat Capacity

Which one stays hot longer after being removed?   Assume equal masses and heat losses. DT = Q/mc

Substance   Specific Heat  Marble        0.90  Aluminum        0.215  Copper        0.092

   Why Hot Apple Pies Burn

ccrust / capple  < 1

Comparing equal masses m, and assuming the same Q loss: DTapple = Q/mcapple DTcrust = Q/mccrust DTapple / DTcrust   = ccrust / capple Apple's temperature drop is smaller than the crust's. (The substance with the higher specific heat capacity stays hot longer.)

  Hot Water Bottle

cwater    =  1.0  cal/g-C calcohol =  0.57 cal/g-C ----------------------------------- Assume both would lose the same heat energy Q in the same time. ----------------------------------- DT = Q/mc Which would be better to keep you warm, a hot-water bottle or a hot-alcohol bottle?

 The Three Phases of Matter

   Phase Transformations

  Latent Heat of Fusion                                            latent:  undisclosed, beneath the surface    

Heat of fusion of H2O:  80 cal/gram

Fusion = melting or freezing  Q = mLf   Question:  How much thermal energy in joules must be absorbed by 50 g of ice at 0 C to melt it? Answer:  50 (80) (4.186) = 16,744 J.   Question:  How much thermal energy will be released when 50 g of water freezes? Answer:  16,744 J.

  Keeping the Greenhouse Warm 

Placing large vats of water in greenhouses protects fruit from freezing; the heat liberated when the water freezes warms the air.

  Keeping the Wolf Cool

Panting wolf rids its body of 540 calories of heat energy with each gram of water vapor it exhales.

   Heat of Fusion

Heat of fusion of gallium = 80 cal/gram Melting point = 29.8 C (85.6 F)

   Heat of Vaporization

Heat of Vaporization:   Water:  Lv  = 540 cal/g --------------------------------------- Question:  How much heat must be added to 20 grams of water at 100 C to convert it to steam?   Answer:   20 g (540 cal/g) = 10,800 cal

   Heat Numbers for H₂0

Ice to ice:                      0.50     cal/g-C  Ice to water:                     80     cal/g    Water to water:              1.0     cal/g-C     Water to steam:           540      cal/g      Steam to steam:          0.48     cal/g-C

 Temperature versus Heat for Water

500 grams of -30 C ice is converted to 500 grams of 300 C steam.  How  many calories are needed?

  Conservation of Energy

Heat lost by hot object = Heat gained by liquid and cup

Example:  100 gram aluminum can with 200 grams of water, all at 20 C.  Add 50 gram of copper at 130 C. What is the final temperature? ------------------------------------------------------- Heat gained by water and aluminum equals heat lost by copper: Solution below:

  Conservation of Energy--continued

Heat gained by water         = (200) (1.000) (T - 20)   (units dropped)         = 200 T - 4000               (positive)

Heat gained by aluminum          = (100 ) (0.215) (T - 20)              = 21.5 T - 430  Heat lost by copper            = (50 ) (0.092) (130 - T)              = 598 - 4.6 T Heat gained = Heat lost (200 T - 4000) + (21.5 T - 430)                = 598 - 4.6 T 226.1 T = 5028           T = 22.24 C