An electric hand mixer draws 1.5 amperes at 110 volts. It is used to mix 1 kg of cookie dough for 5 minutes. After mixing, the temperature of the cookie dough is found to have increased by 5°C. If the heat capacity of the dough is
what fraction of the electrical energy used by the mixer is converted to internal energy of the dough? Discuss the fate of the remainder of the energy.
What will be an ideal response?
The electrical power supplied to the mixer is 1.5 A·110 V = 165 V·A = 165 W. The total energy supplied over a period of 5 minutes is then 5·60·165 = 49500 J = 49.5 kJ. The increase in internal energy of the cookie dough is given by = 21 kJ. Thus, the fraction of the electrical energy that went into heating the cookie dough is 21/49.5 = 0.42; 42% of the energy input has appeared as increased internal energy of the cookie dough. The rest of the energy input has been transferred as heat to the surroundings, or remains as internal energy of the electric mixer, which is probably also at a higher temperature at the end of the process than at the beginning.
From the data given, we know the work input only if the system includes the mixer itself (because we know the current and voltage supplied to it, from which we compute electrical work). Taking the mixer AND the dough as the system, we know W = 49.5 kJ, but we do not separately know Q, the amount of heat transferred between the system and surroundings, or ?U, the change in internal energy of the mixer and dough together.
On the other hand, if we take only the dough as the system, we know that it has = Q +W = 21 kJ, but we do not
know Q and W individually. Here the work done by the mixer on the dough should be some amount smaller than the electrical work provided to the mixer, because the mixer should have some inherent irreversibilities that prevent it from fully converting the incoming electrical work into mechanical work done on the dough.
From the given data, we cannot evaluate all terms in the energy balance for either the dough alone or the mixer and dough together as the system.
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