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Chapter 17. The First Law of Thermodynamics. Heat. Heat is the amount energy transfer due to a temperature difference. All other forms of energy transfer are classified as work. In the picture below, heat is flowing from the hot object to the cold object. Unit of heat.
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Chapter 17 The First Law of Thermodynamics
Heat Heat is the amount energy transfer due to a temperature difference. All other forms of energy transfer are classified as work. In the picture below, heat is flowing from the hot object to the cold object.
Unit of heat People used to think that heat was not the same as energy. Therefore they invented a separate unit for heat, the calorie. 1cal is defined as the heat required to raise the temperature of 1g of water by 1°C. Terminology: cal: little cal Cal: big cal (this is the unit found on food labels)
The equivalence between heat and energy Joule proved that heat is equivalent to energy by the following experiment: He proved that one can raise the temperature of water by doing mechanical work (which involves no temperature difference or heating). He found it took 4.186J of energy to raise the temperature of 1g of water by 1°C, hence 1cal=4.186J.
Specific Heat Capacity 1cal is defined as the heat required to raise the temperature of 1g of water by 1°C.
ΔT in K and in °C Although TK and TC differs by 273 (recall: TK = TC +273), when it comes to ΔT the two scales are the same. That is why in c, it does not matter whether you write 1J kg-1 K-1or 1J kg-1 °C-1 .
More on the units Make sure you know how to convert among the following units: Specific heat capacity is the amount of heat required to raise the temperature of 1kg of a substance by 1K.
Example A 80kg man has a fever of 39°C. How much heat is required to raise his temperature by that amount? [Normal temperature: 37°C, c =4190Jkg-1K-1]
Molar Heat Capacity First a reminder about moles: Define the molar mass M as the mass of one mole of substance, then n moles of the substances would have the mass of:
Change of phase and Latent Heat There is no ΔT in the above equation, because there is no temperature change during phase change. Gas Solid Latent heat of fusion: Energy required to melt 1kg of solid Latent heat of vaporization: Energy required to vaporize 1kg of liquid Latent heat of fusion Liquid Latent heat of vaporization − +
No change in temperature Heat is absorbed during a phase change but the temperature does not change.
Example Find the total amount of energy required to heat 3g of water from -15°C to 155°C.
Soda in an ice box Which will do a better job cooling your soda, a “cooler” filled with water at 0°C, or a cooler filled with ice at 0°C? Water Ice The same
Heat Transfer When two objects are in thermal contact, the heat lost by one is the heat gain by the other by conservation of energy. For example, if QH =-150J, then QC =+150J. In general, we have: If one of the Q is positive, the other must be negative.
Heat Transfer for more objects When there are more than two objects present, then the conservation law earlier generalizes to:
Example 2kg of water at 300K is mixed with 2kg of water at 350K. Find the final temperature.
Example 1.5kg of X at temperature 400K is dropped into 3kg of water at 300K. The final temperature is 360K. Find the specific heat capacity of X.
A student wants to cool 0.25kg of soda, initially at 25°C, by adding ice initially at -20°C. How much ice should be she add so that the final temperature is 0°C with all the ice melted?
Degrees of freedom and Equipartition of energy The result is part of a more general result called the equipartition of energy, which states that each degree of freedom gives rise to a contribution of (1/2)kT per particle. A degree of freedom is each term that appears as x2 or p2 in the energy of the particle, or you can think of it as the number of ways each particle can move.
Counting Degrees of Freedom Air at room temperature has f=5.
Energy of a gas What happens to U when T is changed? How much U is needed to change T by one unit? (This is the total heat capacity only when there is no work W)
