Question

An Isothermal Expansion A 3.0 mol sample of an ideal gas is kept at 0.0°C during an expansion from 3.0 L to 10.0 L. (a) How much work is done on the gas during the expansion? SOLUTION Conceptualize Run the process in your mind: the cylinder in the figure is immersed in an ice-water bath, and the piston moves outward so that the volume of the gas ---Select--- . You can also use the graphical representation shown above to conceptualize the process. Categorize We will evaluate parameters using equations developed in the preceding sections, so we categorize this example as a substitution problem. Because the temperature of the gas is fixed, the process is ---Select--- . Substitute the given values into the following equation (Enter your answer in J): W = nRT ln(Vi/Vf) = J (b) How much energy transfer by heat occurs between the gas and its surroundings in this process? SOLUTION Find the heat from the first law (Enter your answer in J): ?Eint = Q + W 0 = Q + W Q = -W = J (c) If the gas is returned to the original volume by means of an isobaric process, how much work is done on the gas? SOLUTION Use W = -P(Vf - Vi). The pressure is not given, so incorporate the ideal gas law (Enter your answer in J. Note the initial and final volumes for this process are different than for the process in part (a).): W = -P(Vf - Vi) = -nRTi/Vi (Vf - Vi) = J EXERCISE We now consider three moles of ideal gas at the same initial state (3.0 L at 273 K). This time, we will first perform an isobaric compression, then an isothermal expansion to bring the gas to the final state with the same volume of 3.0 L, and at temperature 130 K. Hint (a) How much work (in J) is done on the gas during the isobaric compression? Wcompression = J (b) How much work (in J) is done on the gas during the isothermal expansion? Wexpansion = J

          An Isothermal Expansion
A 3.0 mol sample of an ideal gas is kept at 0.0°C during an expansion from 3.0 L to 10.0 L.
(a) How much work is done on the gas during the expansion?
SOLUTION
Conceptualize Run the process in your mind: the cylinder in the figure is immersed in an ice-water bath, and the piston moves outward so that the volume of the gas ---Select--- . You can also use the graphical representation shown above to conceptualize the process.
Categorize We will evaluate parameters using equations developed in the preceding sections, so we categorize this example as a substitution problem. Because the temperature of the gas is fixed, the process is ---Select--- .
Substitute the given values into the following equation (Enter your answer in J):
W = nRT ln(Vi/Vf) = J
(b) How much energy transfer by heat occurs between the gas and its surroundings in this process?
SOLUTION
Find the heat from the first law (Enter your answer in J):
?Eint = Q + W
0 = Q + W
Q = -W = J
(c) If the gas is returned to the original volume by means of an isobaric process, how much work is done on the gas?
SOLUTION
Use W = -P(Vf - Vi). The pressure is not given, so incorporate the ideal gas law (Enter your answer in J. Note the initial and final volumes for this process are different than for the process in part (a).):
W = -P(Vf - Vi) = -nRTi/Vi (Vf - Vi) = J
EXERCISE
We now consider three moles of ideal gas at the same initial state (3.0 L at 273 K). This time, we will first perform an isobaric compression, then an isothermal expansion to bring the gas to the final state with the same volume of 3.0 L, and at temperature 130 K.
Hint
(a) How much work (in J) is done on the gas during the isobaric compression?
Wcompression = J
(b) How much work (in J) is done on the gas during the isothermal expansion?
Wexpansion = J

An Isothermal Expansion
A 3.0 mol sample of an ideal gas is kept at 0.0°C during an expansion from 3.0 L to 10.0 L.
(a) How much work is done on the gas during the expansion?
SOLUTION
Conceptualize Run the process in your mind: the cylinder in the figure is immersed in an ice-water bath, and the piston moves outward so that the volume of the gas —Select— . You can also use the graphical representation shown above to conceptualize the process.
Categorize We will evaluate parameters using equations developed in the preceding sections, so we categorize this example as a substitution problem. Because the temperature of the gas is fixed, the process is —Select— .
Substitute the given values into the following equation (Enter your answer in J):
W = nRT ln(Vi/Vf) = J
(b) How much energy transfer by heat occurs between the gas and its surroundings in this process?
SOLUTION
Find the heat from the first law (Enter your answer in J):
?Eint = Q + W
0 = Q + W
Q = -W = J
(c) If the gas is returned to the original volume by means of an isobaric process, how much work is done on the gas?
SOLUTION
Use W = -P(Vf - Vi). The pressure is not given, so incorporate the ideal gas law (Enter your answer in J. Note the initial and final volumes for this process are different than for the process in part (a).):
W = -P(Vf - Vi) = -nRTi/Vi (Vf - Vi) = J
EXERCISE
We now consider three moles of ideal gas at the same initial state (3.0 L at 273 K). This time, we will first perform an isobaric compression, then an isothermal expansion to bring the gas to the final state with the same volume of 3.0 L, and at temperature 130 K.
Hint
(a) How much work (in J) is done on the gas during the isobaric compression?
Wcompression = J
(b) How much work (in J) is done on the gas during the isothermal expansion?
Wexpansion = J

Added by Jeffrey B.

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