An electric pressure cooker is fitted with a 10.75 ohms resistance, and connected to a 127-V outlet. The cooker is originally filled with 2.5 kg of ice at -15ΒΊ C. At t = 0, the device is turned on. The safety valve is set up so a constant pressure of 1 atm. will exist within the cooker at all times, and it may be assumed that all the energy produced by the resistance is transmitted to the ice and/or water in the cooker, and that there is no energy exchange with the environment. You are asked to do the following:
Calculate the time at which all the ice will be melted, and the time at which all the water inside the cooker will be evaporated.
Best answer:
Answer by Felicia
law of energy conservation
Qin = Qout
Q input is the electric pressure cooker. it has power P=V.I= V. (V/R) = V^2.R. power is energy flow per time unit, so input energy Qin = P.t = V^2.R . t
Q output is the energy, in the form of heat, transferred to the ice. we need to know how much energy in heat form is needed to melt m= 2.5kg of T1= -15 C ice
ice melting at 0 C...there is dualism at 0 degree celcius; water can either be in solid form, or liquid/melted form.
first we need to calculate the energy needed to increase the temperature of ice from T1= -15 to T2= 0 C.
the formula is Q ice = m.c. (T2 - T1) where c is heat capacity of ice. you can google it.
now we have 2.5kg of 0 degree C ice. now we need to melt it. in state transforming process, there is no change of temperature, since the energy is used for transforming, in this case, ice to water
the amount of energy needed for this transformation is:
Q melt = m.L where L is the amount of energy in KJ or J needed in order to transform one kilogram of ice to water. google it too.
so the total energy needed to melt the ice is
Qout = Q ice + Q melt = m.c.(T2 - T1) + m.L
Qin = Q out
V^2.R. t = m.c.(T2 - T1) + m.L
there it is, you get t. t is the amount of time you need to melt the ice using your pressure cooker.
to find the time at which all water will be evaporated, the same thing goes for second process. but note these: now the initial temperature of the water is T1= 0 C we want to have this water transformed to steam, that is T2= 100 C,
and now L is the amount of energy in KJ or J needed in order to transform one kilogram of water to vapour.
sorry no calculation, i don't have my calculator at hand. hope this clear enough
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