Heat Capacity

Heat In This is comparable to work done on a system. Temperature change is due to heat (Q). If an object’s temperature increases it gains heat. If an object’s temperature decreases it loses heat. This is comparable to work done on a system. Heat into a system

Heat Capacity The ratio of the change in heat to the change in temperature is the heat capacity (C). Depends on material Depends on the mass Measured in J/K

Specific Heat The ratio of the change in heat to the change in temperature is the heat capacity (C). Depends on material independent of the mass Measured in J/kg-K Material Specific heat Mercury 140 J/kg-K Copper 390 J/kg-K Steel 500 J/kg-K Granite 840 J/kg-K Aluminum 900 J/kg-K Wood 1400 J/kg-K Ice 2100 J/kg-K Water 4200 J/kg-K

Take a Shower You are last to use the shower today and the temperature in the water heater has dropped to 18 C from the normal temperature of 50 C. The heater holds 150 kg and has a 50 kW heating coil. How long should you wait before starting your shower? Find the heat required. DQ = mcDT = (150 kg) (4200 J/kg-K) ( 32 C) DQ = 2.1 x 107 J Find the time from the power, and set the heat to the work. P = DW/Dt t = DQ / P (2.1 x 107 J) / (5 x 104 W) t = 4000 s = 1.1 hr

Equilibrium Temperature Two systems in thermal contact will adjust to reach the same temperature - thermal equilibrium If they are thermally insulated, all the heat goes from the hot system to the cold system. 1 2

Doing Dishes A 1.5 kg aluminum pan is heated to 180 C then placed into a sink with 8 kg water at 20 C. If no water boils, what is the equilibrium temperature? Setup the equation for an unknown equilibrium temperature T. Solve for T. T = 26 C

Heat of Transformation As a system reaches the point of a phase change heat no longer changes the temperature. The heat is used to change the phase. heat of fusion heat of vaporization

Latent Heat The heat of transformation per unit mass is called the latent heat (L). Measured in J/kg It takes as much energy to melt 1 g of ice as it does to raise the temperature from 0 C to 80 C. Material (f or v) Latent Heat Mercury (f) 11.3 kJ/kg Lead (f) 24.7 kJ/kg Uranium (f) 82.8 kJ/kg Copper (f) 205 kJ/kg Water (f) 334 kJ/kg Oxygen (v) 213 kJ/kg Water (v) 2300 kJ/kg

Summer Cooler 200 g of ice at -10 C is added to 1.0 kg of water at 15 C. Is there enough ice to cool the water to 0 C? Find the amount of heat needed to bring the ice to 0 C and melt it. Qi = mcDT + mLf Qi = 70.9 kJ Find the heat needed to cool the water down to 0 C. Qw = mcDT Qw = 62.8 kJ Yes, there’s enough ice.