Figure 20-6 is the
(a)
The temperature of the gas at B, if the temperature at A is
Answer to Problem 52SP
Solution:
Explanation of Solution
Given data:
Refer to Fig. 20-6.
The temperature at A is
The mass of the ideal gas enclosed is
The specific heat of the gas at constant volume is
The gas follows the process A to B in the thermodynamic cycle shown in Fig. 20-6.
Formula used:
The gas equation between initial and final condition of a gas can be written as,
Here,
The formula for the conversion of the initial temperature of a gas from the Celsius scale to the Kelvin scale is,
Here,
The area of a trapezium is calculated by the formula,
Here,
The work done in a thermodynamic process is given by the area under the line representing the process in the pressure-volume diagram.
Here,
Explanation:
Draw the thermodynamic cycle diagram given in Fig- 20.6.
Recall the expression for the conversion of temperature at A from Celsius to Kelvin.
Here,
Substitute
Refer to the diagram and write the values of pressure and volume at points A and B, respectively.
And,
Here,
Recall the gas equation between points A and B.
Here,
Substitute
Conclusion:
The temperature at point B is
(b)
The value of
Answer to Problem 52SP
Solution:
Explanation of Solution
Given Data:
Refer to Fig. 20-6.
The temperature at A is
The mass of the ideal gas enclosed is
The specific heat of the gas at constant volume is
Formula Used:
The formula for change in internal energy is,
Here,
The formula for conversion of temperature of gas from Kelvin scale to Celsius scale is,
Here,
Explanation:
Draw the thermodynamic cycle diagram given in Fig- 20.6.
Calculate the temperature at point B in Celsius.
Here,
Substitute
Calculate the change in temperature from A to B.
Substitute
Recall the formula for change in internal energy.
Substitute
Conclusion:
The value of
(c)
The value of
Answer to Problem 52SP
Solution:
Explanation of Solution
Given Data:
Refer to Fig. 20-6.
The temperature at A is
The mass of the ideal gas enclosed is
The specific heat of the gas at constant volume is
Formula Used:
The area of a trapezium is calculated by the formula,
Here,
The work done in a thermodynamic process is given by the area under the line representing the process in the pressure-volume diagram.
Here,
Explanation:
Draw the thermodynamic cycle diagram given in Fig- 20.6.
Understand that the work done in the thermodynamic process AB is equal to the area of the pressure-volume diagram under the line AB.
Draw the thermodynamic cycle diagram showing the area under the line AB.
Here, the points E and F are as shown in the figure and the work done during the process AB is represented by the area under the line AB, which is equal to the area of the trapezium ABEF.
Refer to the figure and write the values of the lengths of sides AF, BE, and EF.
Recall the expression for the area of trapezium ABEF to calculate the area under the line AB in order to calculate the work done in the process AB.
Here,
Substitute
Recall the expression for the net-work done in a thermodynamic process in terms of the area of the pressure-volume diagram.
Substitute
The work done from A to B is
Conclusion:
The value of
(d)
The value of
Answer to Problem 52SP
Solution:
Explanation of Solution
Given Data:
Refer to Fig. 20-6.
The temperature at A is
The mass of the ideal gas enclosed is
The specific heat of the gas at constant volume is
Formula Used:
The first law of thermodynamics for a process is written as,
Here,
Explanation:
Draw the thermodynamic cycle diagram given in Fig- 20.6.
Recall the expression for the first law of thermodynamics for the process AB.
Substitute
Conclusion:
The value of
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Chapter 20 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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