Which of the following functions are exact differentials?
(a)
(b)
(c)
(d)
(e)
(f)
(a)
Interpretation:
Whether the function,
Concept introduction:
A function is said to be an exact differential if it satisfies the relation given below.
In the above equation,
Answer to Problem 4.36E
The given function,
Explanation of Solution
The given function is written below.
Using the identity of exact differential, the function can be differentiated as shown below.
Since,
The given function,
(b)
Interpretation:
Whether the function,
Concept introduction:
A function is said to be an exact differential if it satisfies the relation given below.
In the above equation,
Answer to Problem 4.36E
The given function,
Explanation of Solution
The given function is written below.
Using the identity of exact differential, the function can be differentiated as shown below.
Since,
The given function,
(c)
Interpretation:
Whether the function,
Concept introduction:
A function is said to be an exact differential if it satisfies the relation given below.
In the above equation,
Answer to Problem 4.36E
The given function,
Explanation of Solution
The given function is written below.
Using the identity of exact differential, the function can be differentiated as shown below.
Since,
The given function,
(d)
Interpretation:
Whether the function,
Concept introduction:
A function is said to be an exact differential if it satisfies the relation given below.
In the above equation,
Answer to Problem 4.36E
The given function,
Explanation of Solution
The given function is written below.
Using the identity of exact differential, the function can be differentiated as shown below.
Since,
The given function,
(e)
Interpretation:
Whether the function,
Concept introduction:
A function is said to be an exact differential if it satisfies the relation given below.
In the above equation,
Answer to Problem 4.36E
The given function,
Explanation of Solution
The given function is written below.
Using the identity of exact differential, the function can be differentiated as shown below.
Since,
The given function,
(f)
Interpretation:
Whether the function,
Concept introduction:
A function is said to be an exact differential if it satisfies the relation given below.
In the above equation,
Answer to Problem 4.36E
The given function,
Explanation of Solution
The given function is written below.
Using the identity of exact differential, the function can be differentiated as shown below.
Since,
The given function,
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Chapter 4 Solutions
Student Solutions Manual for Ball's Physical Chemistry, 2nd
- Snitial Sinal В Sfinal A Sanal Sfinal 13V3 Based on the image, which system has a AS of zero?arrow_forwardYou have the following data points which belong to a function of the form y = ae"¸ where b can be positive or negative. 3.59 2.52 1.77 0.100 0.200 0.300 You wish to determine the value of the constant, b, and to do so you will construct a linear plot. What will you plot against what? y-axis label: Iny - T-axis label: x From the values of a and y in the table above, calculate the values of the three corresponding data points. Click on the graph below, and use the "Freeform Curves" tool to plot the data. Line segments will automatically connect the points. Enter Solution What is the numerical value of the constant, b? Previous Nextarrow_forwardA2. Determine total differentials: dT = dT(s,v), dP = dP(s, v), dụ = dµ(s,v). %|arrow_forward
- B–3. An important continuous distribution is the exponential distribution p(x)dx = ce 0 a.arrow_forwardthe linear trendline equation y= 4.7033x + 0.0045arrow_forwardnRT (c) Consider the following differential: dq = nC, dT +“A dV, where n and R are constants. V (i) Is the above differential dq, an exact or inexact differential? [Show how you arrived to your conclusion by evaluating the appropriate partial differentials!!]arrow_forward
- Suppose we put an object with temperature T0 in a room with constant temperature K.We know that the heating/cooling speed of the object is proportional to the temperature differencebetween the object and the environment with ratio r a positive constant. If we write the temperature of the object T as a function of time t, write out the differentialequation it has to satisfy.arrow_forwardThe explanation Cannot be hand-drawn must be typed Answer 2C (look at 2a, and 2b for all relevant data)arrow_forwardA cable that weighs 4 lb/ft is used to lift 850 lb of coal up a mine shaft 300 ft deep. Find the work done. Show how to approximate the required work by a Riemann sum. (Let x be the distance in feet below the top of the shaft. Enter x;* as x₁.) lim 818 i = 1 1) AX Ax Express the work as an integral. 6 Evaluate the integral. ft-lb. dxarrow_forward
- Physical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,