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(a) The pV-diagram which shows a cycle of a heat engine that uses 0.250 mol of an ideal gas with g = 1.40. Process ab is adiabatic. (i) Find the pressure of the gas at point a. (ii) How much heat enters this gas per cycle, and where does it happen? (iii) How much heat leaves this gas in a cycle, and where does it occur? (iv) How much work does this engine do in a cycle? (v) What is the thermal efficiency of the engine?
(b) Freezer has a coefficient of performance of 2.40. The freezer is to convert 1.80 kg of water at 25 degrees Celsius to 1.80 kg of ice at -5.0 degrees Celsius in one hour. (i) What amount of heat must be removed from the water at 25 degrees Celsius to convert it to ice at -5.0 degrees Celsius? (ii) How much electrical energy is consumed by the freezer during this hour? (iii) How much wasted heat is delivered to the room in which the freezer sits?
- suppose that a heat engine is connected to two energy reservoirs, one a pool of molten aluminum (660 degrees Celsius) and the other a block of solid mercury (-38.9 degrees Celsius). 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 3.97 X 105 J/kg; the heat of fusion of mercury is 1.18 X 104 J/kg. What is the efficiency of this engine?
- Argon enters a turbine at a rate of 80.0 kg/min, a temperature of 800 degrees Celsius 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.
(b) Calculate the (maximum) the
power output of the turning turbine.
(c) The turbine is one component of a
model closed-cycle gas turbine
engine . Calculate the maximum
efficiency of the engine.
A constant volume gas thermometer containing helium gives readings of gas pressure, ‘p’ of 1000 and 1366 mm of mercury at the ice point and the steam point respectively.
(a) Express the gas thermometer Celsius temperature, ‘tc’ in terms of gas pressure p.
(b) The thermometer, when left standing in the atmosphere, registers 1075 mm. Determine the
atmospheric temperature.
Two moles of an ideal gas occupy a volume V. The gas expands isothermally and reversibly to a volume
3V. (a) Is the velocity distribution changed by the isothermal expansion? Explain. (b) Use Eq.
(Microscopic state) to calculate the change in entropy of the gas. (c) Use Eq. (reversible isothermal
process) to calculate the change in entropy of the gas. Compare this result to that obtained in part (b).
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.
