7) When water initially at a temperature T1 is mixed with the same amount of water at a different temperature T2 in an insulated container at constant pressure, the final temperature of the mixture is the average of the two. Show that the change in entropy for the adiabatic mixing process is given by AS = C, In C +T; )² 4T;T, hat AS is always positive for any values of the two initial temperatures provided that they are same.

7) When water initially at a temperature T1 is mixed with the same amount of water at a different temperature T2 in an insulated container at constant pressure, the final temperature of the mixture is the average of the two. Show that the change in entropy for the adiabatic mixing process is given by AS = C, In C +T; )² 4T;T, hat AS is always positive for any values of the two initial temperatures provided that they are same.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter4: The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 52P: (a) A 5.0-kg rock at a temperature of 20 is dropped into a shallow lake also at 20 from a height...

See similar textbooks

Similar questions

A copper rod of cross-sectional area 5.0 cm2 and length 5.0 m conducts heat from a heat reservoir at 373 K to one at 273 K. What is the time rate of change of the universe's entropy for this process?
Is it possible for a system to have an entropy change if it neither absorbs nor emits heat during a reversible? transition? What happens it the process is irreversible?
In an isochoric process, heat is added to 10 mol of monoatomic ideal gas whose temperature increases from 273 to 373 K. What is the entropy change of the gas?
In a diesel engine, the fuel is ignited without a spark plug. Instead, air in a cylinder is compressed adiabatically to a temperature above the ignition temperature of the fuel; at the point of maximum compression, the fuel is injected into the cylinder. Suppose that air at 20 C is taken into the cylinder at a volume V1 and then compressed adiabatically and quasi-statically to a temperature of 600 C and a volume V2 . If =1.4 , what is the ratio V1/V2 ? (Note: static. In an operating diesel engine, the compression is not quasi-
A glass beaker of mass 400 g contains 500 g of water at 27 . The beaker is heated reversibly so that the temperature of the beaker and water rise gradually to 57 . Find the change in entropy of the beaker and water together.
(a) infinitesimal amount of heat is added reversibly to a system. By combining the first and second laws, show that dU=TdSdW. (b) When heat is added to an ideal gas, its temperature and volume change from T1 and V1 to T2 and V2 . Show that the entropy change of n moles of the gas is given by S=CnvlnT2T1nRlnV2V1 .
For the Carnot cycle of Figure 4.12, what is the entropy change of the hot reservoir, the cold reservoir, and the universe? Figure 4.11 The four processes of the Carnot cycle. The working substance is assumed to be an ideal gas whose thermodynamic path MNOP is represented in Figure 4.12. Figure 4.12 The total work done by the gas in the Carnot cycle is shown and given by the area enclosed by the loop MNOPM.
(a) A 5.0-kg rock at a temperature of 20 is dropped into a shallow lake also at 20 from a height of 1.0103 m. What is the resulting change in entropy of the universe? (b) If the temperature of the lock is 100 when it is dropped, what is the change of entropy of the universe? Assume that air friction is negligible (not a good assumption) and that c=860 J/kg K is the specific heat of the rock.
Suppose 20 g of ice at 0 is added to 300 g of water at 60 . What is the total change in entropy of the mixture after it reaches thermal equilibrium?
A cylinder containing three moles of a monatomic ideal gas is heated at a constant pressure of 2 atm. The temperature of the gas changes from 300 K to 350 K as a result of the expansion. Find work done (a) on the gas; and (b) by the gas.
A 0.50-kg piece of aluminum at 250 is dropped into 1.0 kg of water at 20 . After equilibrium is reached, what is the net entropy change of the system?
A monatomic ideal gas undergoes a quasi-static process that is described by the function pV=p1+3(vv1) , where the stating state is (p1,v1) and the final state (p2,v2) . Assume the system consists of n moles of the gas in a container that can exchange heat with the environment and whose volume can change freely. (a) Evaluate the work done by the gas during the change in the state. (b) Find the change in internal energy of the gas. (c) Find the heat input to the gas during the change. (d) What ale initial and final temperatures?