physics 19.2 specific heat capacity

what does the temperature rise of an object when it is heated depend on

the mass of the object; the amount of energy supplied to it; the substance or substances from which the object is made

the specific heat capacity of a substance, c

the energy needed to raise the temperature of unit mass of the substance by 1K without change of state, J/kgK

equation for the energy needed to raise the temperature of mass m of a substance from temperature T1 to temperature T2

ΔQ = mc(T2 - T1)

what takes place in the inversion tube experiment

the gravitational potential energy of an object falling in a tube is converted into internal energy when it hits the bottom of a tube; the tube is inverted each time the spheres hit the bottom of the tube; the temperature of the object is measured initially and after a particular number of inversions

equation for the loss of gravitational potential energy for n inversions in the inversion tube experiment

loss of gpe = mgLn, where m is the mass of the lead shot(object), and L is the length of the tube

equation for the gain of internal energy of the lead shot (object) in the inversion tube experiment

gain of internal energy = mcΔT, where c is the specific heat capacity of lead, and ΔT is the temperature rise of the lead shot

equation for the specific heat capacity of the lead shot (object) in the inversion tube experiment, given by equating the 2 equations

mcΔT = mgLn --> c = gLn/ΔT

experiment for measuring the specific heat capacity of a metal

a block of metal of known mass m in an insulated container is used; a 12V electrical heater is inserted into a hole drilled into the metal + supplies a known amount of electrical energy; a thermometer is inserted into a second hole drilled in + is used to measure the temperature rise ΔT

how can the thermal contact between the thermometer and the metal be improved in the experiment measuring specific heat capacity of a metal

a small amount of water/oil can be placed in the thermometer hole

equation for the electrical energy supplied by the electric heater to the metal block in the experiment for measuring specific heat capacity

electrical energy supplied = heater current, I, x heater pd, V, x heating time, t --> Q = IVt

equation for specific heat capacity of a metal block in the experiment for measuring specific heat capacity, given by equating the 2 equations

assuming no heat loss to the surroundings, mcΔT=IVt --> c=IVt/mΔT

experiment for measuring the specific heat capacity of a liquid

a known mass of the liquid is used in an insulated calorimeter of known mass and known specific heat capacity; a 12V electrical heater is placed in the liquid and used to heat it directly; a thermometer inserted into the liquid is used to measure the temperature rise ΔT

equation for the electrical energy supplied in the experiment for measuring specific heat capacity of a liquid

electrical energy supplied = current I x voltage V x heating time t --> Q=IVt

equation for the energy needed to heat the liquid in the experiment for measuring specific heat capacity of a liquid

energy = mass of liquid m1 x specific heat capacity of liquid c1 x temperature rise ΔT --> Q=m1c1ΔT

equation for energy needed to heat the calorimeter in the experiment for measuring specific heat capacity of a liquid

energy - mass of calorimeter m2 x specific heat capacity of calorimeter c2 x temperature rise ΔT --> Q=m2c2ΔT

an electric shower as an example of continuous flow heating

water passes steadily through copper coils heated by an electric heater, + so the water is hotter at the outlet than at the inlet - when the outflowing water has attained a steady temperature, the temperature of the copper coils doesn't change

equation for the electrical energy supplied per second for mass m of a liquid passing through a heater in time t at a steady flow rate, assuming no heat loss to the surroundings

electrical energy supplied per second, IV = mcΔT/t

equation for the energy gained per second by heating the liquid that flows through a solar heating panel

energy = mcΔT/t