Question

An ideal gas is taken through the four processes shown in the figure(Figure 1). The changes in internal energy for three of these processes are as follows: ΔUAB = 89 J ; ΔUBC = 18 J ; ΔUDA = -53 J . Figure1 of 1 The figure shows four processes for an ideal gas in a pressure versus volume plot. Pressure is marked on the y axis. Volume is marked on the x axis. Four states of the ideal gas are marked with points A, B, C, and D. A curve between any two adjacent points represents a process of the ideal gas with its direction from the first point to the second one. The curve A B is a line parallel to the x axis. The curve B C is a line parallel to the y axis, which is shorter than line A B. The curve C D is a top semicircle such that point D is on the left of point C and on the right of and above point A. The curve D A is a linearly decreasing line. The area of figure A B C D is shaded. Part A Find the change in internal energy for the process from C to D .An ideal gas is taken through the four processes shown in the figure(Figure 1). The changes in internal energy for three of these processes are as follows: ΔUAB = 89 J ; ΔUBC = 18 J ; ΔUDA = -53 J . Figure1 of 1 The figure shows four processes for an ideal gas in a pressure versus volume plot. Pressure is marked on the y axis. Volume is marked on the x axis. Four states of the ideal gas are marked with points A, B, C, and D. A curve between any two adjacent points represents a process of the ideal gas with its direction from the first point to the second one. The curve A B is a line parallel to the x axis. The curve B C is a line parallel to the y axis, which is shorter than line A B. The curve C D is a top semicircle such that point D is on the left of point C and on the right of and above point A. The curve D A is a linearly decreasing line. The area of figure A B C D is shaded. Part A Find the change in internal energy for the process from C to D .

Answer 1

ΔUCD = 160 J

Step-by-step explanation:

We know the change in internal energy from point A to point B is ΔUAB = 89 J, the change in internal energy from point B to point C is ΔUBC = 18 J, and the change in internal energy from point A to point D is ΔUDA = 53 J.

To find the change in internal energy for the process from point C to point D, we can substract the change in internal energy from point A to point D (ΔUDA) from the sum of the changes in internal energy from point A to point B (ΔUAB) and from point B to point C (ΔUBC)

This can be expressed as:

"ΔUCD = (ΔUAB + ΔUBC) - ΔUDA"

Substituting the given values, we have:

"ΔUCD = (89 J + 18 J) - (53 J)"

Simplifying, we get:

"ΔUCD = 107 J + 53 J"

"ΔUCD = 160 J"