a) How much work is done on the gas as the temperature of 0.155 mol of the gas is raised from 30.0° to 340°C?
b) What does the sign of your answer to part (a) indicate?
- the gas does positive work on its surroundings
- there is no work done, by the gas or the surroundings
- The surroundings do positive work on the gas
2. Gas in a container is at a pressure of 1.8 atm and the volume of 9.0 m3.
a) What is the work done on the gas if it expands at constant pressure to twice its initial volume?
b) What is the work done on the gas if it is compressed at constant pressure to one quarter of its initial volume?
3.A gas expands from I to F along the three paths indicated in the figure below. Calculate the work done on the gas along each of the following paths.
4. One mole of an ideal gas initially at a temperature of Ti = 1.8°C undergoes an expansion at a constant pressure of 1.00 atm to three times its original volume
a) Calculate the new temperature Tf of the gas.
b) Calculate the work done on the gas during the expansion.
5. One mole of an ideal gas initially at a temperature of 1.50 x 102°C is compressed at a constant pressure of 2.00 atm to two-thirds its initial volume.
a) What is the final temperature of the gas?
b) Calculate the work done on the gas during the compression.
6. An ideal gas in a cylinder is compressed very slowly to one-third its original volume while its temperature is held constant. The work required to accomplish this task is 64 J.
a) What is the change in the internal energy of the gas?
b) How much energy is transferred to the gas by heat in this process?
7. A gas is compressed at a constant pressure of 0.800 atm from 9.00 L to 2.00 L. In the process, 390 J of energy leaves the gas by heat.
a) What is the work done on the gas?
b) What is the change in its internal energy?
8. Five moles of gas initially at a pressure of 2.00 atm and a volume of 0.300 L has internal energy equal to 82.0 J. In its final state, the gas is at a pressure of 1.50 atm and a volume of 0.800 L, and its internal energy equals 168 J.
a) For the paths IAF, IBF, and IF in the figure above, calculate the work done on the gas.
WIAF = ______ J
WIBF = ______ J
WIF = ______ J
b) For the paths IAF, IBF, and IF in the figure above, calculate the net energy transferred to the gas by heat in the process.
QIAF = _____ J
QIBF = _____ J
QIF = _____ J
9. A heat engine operates between a reservoir at 24°C and one at 439°C. What is the maximum efficiency possible for this engine?
10.In each cycle of its operation, a heat engine expels 3,000 J of energy and performs 1,700 J of mechanical work.
a) How much thermal energy must be added to the engine in each cycle
b) Find the thermal efficiency of the engine.
11. One of the most efficient engines ever built is a coal-fired steam turbine engine in the ohio valley, driving an electric generator as it operates between 1870°C and 430°C.
a) What is its maximum theoretical efficiency?
b) Its actual efficiency is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.8 x 105 J of energy each second from the hot reservoir?
12. An engine absorbs 1.68 kJ from a hot reservoir at 277°C and expels 1.16 kJ to a cold reservoir at 27°C in each cycle.
a) What is the engine's efficiency?
b) How much work is done by the engine in each cycle?
c) What is the power output of the engine if each cycle lasts 0.305 s?
13. A heat pump has a coefficient of performance of 3.75 and operates with a power consumption of 6.90 x103 W.
a) How much energy does it deliver into a home during 6 h of continuous operation?
b) How much energy does it extract from the outside air?
14. A heat engine operates in a Carnot cycle between 82.0°C and 340°C. It absorbs 21,600 J of energy per cycle from the hot reservoir. The duration of each cycle is 4.00 s.
a) What is the mechanical power output of this engine?
b) How much energy does it expel in each cycle by heat?