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An ice-making machine operates in a Carnot cycle. It takes heat from water at 0.0°C and rejects heat to
a room at 24.0°C. Suppose that 85.0 kg of water at 0.0_C are converted to ice at 0.0°C. (a) How much
heat is discharged into the room? (b) How much energy must be supplied to the device?
You make tea with 0.250 kg of 85.0°C water and let it cool to room temperature (20.0°C). (a) Calculate
the entropy change of the water while it cools. (b) The cooling process is essentially isothermal for the
air in your kitchen. Calculate the change in entropy of the air while the tea cools, assuming that all of
the heat lost by the water goes into the air. What is the total entropy change of the system tea + air?
freezer has a coefficient of performance of 2.40. The freezer is to convert 1.80 kg of water at 25.0°C to
1.80 kg of ice at -5.0°C in one hour. (a) What amount of heat must be removed from the water at 25.0°C
to convert it to ice at -5.0°C? (b) How much electrical energy is consumed by the freezer during this
hour? (c) How much wasted heat is delivered to the room in which the freezer sits?
Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800°C, and a pressure of 1.50 MPa. It
expands adiabatically as it pushes on the turbine blades and exits at a pressure of 300 kPa.
(a) Calculate its temperature at the time of exit. [5]
(b) Calculate the (maximum) power output of the turning turbine. [5]
(c) The turbine is one component of a model closed-cycle gas turbine engine. Calculate the maximum
efficiency of the engine.
Suppose that a heat engine is connected to two energy reservoirs, one a pool of molten aluminum
(660°C) and the other a block of solid mercury (-38.9°C). The engine runs by freezing 1.00 g of
aluminum and melting 15.0 g of mercury during each cycle. The heat of fusion of aluminum is 3.97x105
J/kg; the heat of fusion of mercury is 1.18 x104 J/kg. What is the efficiency of this engine?
- One hundred unit point masses are connected with identical linear springs of unit stiffness
on a circular ring of unit radius. Find the largest angular frequency of oscillations of the masses.
- One mole of argon (assumed to be an ideal gas) expands according to the relation p =
kV between its pressure and volume,k = const. Find the entropy change of the gas when its volume
doubles.
A steel I-beam used in the construction of a bridge is 9.2m long at 20°C. On a hot summer day, the temperature rises to 40°C. What is the change in the beam's length due to linear expansion?
a. shows a bead sliding on a wire, How large must height h1 be if the bead, starting at rest A, is to have a velocity of 200cm/s at point B? Ignore friction
One liter of water at 46◦C is used to make iced tea. How much ice at 0 ◦C must be added to lower the temperature of the tea to 19 ◦C? The specific heat of water is 1 cal/g · ◦ C and latent heat of ice is 79.7 cal/g. Answer in units of g.
How much energy is required to change a 39 g ice cube from ice at −14◦C to steam at 114◦C? The specific heat of ice is 2090 J/kg · ◦ C, the specific heat of water is 4186 J/kg · ◦ C, the specific heat of stream is 2010 J/kg · ◦ C, the heat of fusion is 3.33 × 105 J/kg, and the heat of vaporization is 2.26 × 106 J/kg. Answer in units of J.
