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In this lesson, we will learn how to calculate the change in the entropy of a system that results from various thermodynamic processes.

Q1:

Find the entropy change of 20 g of steam at a temperature of 1 0 0 ∘ C when it condenses to water at the same temperature. Use a value of 2 2 5 7 kJ/kg for the latent heat of vaporization of water.

Q2:

A cube of ice with a mass of fifty grams and at a temperature of 0 . 0 0 ∘ C is allowed to melt to become water, and then boil to become water vapour at 1 0 0 ∘ C . What is the change in entropy of the water in this process?

Q3:

2 . 0 0 × 1 0 2 joules of heat is removed from a heat reservoir at a temperature of 2 . 0 0 × 1 0 2 K. What is the entropy change of the reservoir?

Q4:

A system consisting of 20.0 mol of a monoatomic ideal gas is cooled at constant pressure from a volume of 50.0 L to a volume of 10.0 L. The initial temperature of the gas was 300 K. What is the change in entropy of the gas?

Q5:

An ideal gas at a temperature of 3 . 0 × 1 0 2 K is compressed isothermally to a volume that is 0.20 times its initial volume. Determine the entropy change per mole of the gas.

Q6:

A 2.00 × 10^{2}-g mass of water at a temperature of 0 . 0 0 ∘ C is brought into thermal equilibrium successively with reservoirs at 2 0 . 0 ∘ C , 4 0 . 0 ∘ C , 6 0 . 0 ∘ C , and 8 0 . 0 ∘ C . Use a value of 4 1 8 2 / ⋅ J k g C ∘ for the specific heat capacity of water.

What is the entropy change of the water?

What is the entropy change of the reservoirs?

What is the entropy change of the universe?

Q7:

A Carnot engine operates between baths with temperatures of 5 5 0 ∘ C and 2 0 ∘ C , and extracts 300 kJ of energy in each cycle.

Find the change in entropy of the hot bath in each Carnot cycle.

Find the change in entropy of the cold bath in each Carnot cycle.

Q8:

A copper rod of cross-sectional area 5.0 cm^{2} 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? Use a value of 385 W/m⋅K for the thermal conductivity of copper.

Q9:

A piece of aluminium of mass 0.50 kg is at a temperature of . The aluminium is dropped into a 1.0 kg mass of water that is at a temperature of . After equilibrium is reached, what is the net entropy change of the system? Use a value of as the specific heat capacity of water and a value of as the specific heat capacity of aluminium.

Q10:

A 200-g-mass of water a temperature of 0 . 0 0 ∘ C is brought into contact with a heat reservoir at a temperature of 8 0 . 0 ∘ C , and thermal equilibrium is reached. Use a value of 4 1 8 0 / ⋅ J k g C ∘ for the specific heat capacity of water.

What is the temperature of the water?

What is the temperature of the reservoir?

How much heat has been transferred in the process?

What is the entropy change of reservoir?

Q11:

For the Carnot cycle in the figure, consider the efficiency to be 0.65 and the heat consumed per cycle to be 300 J.

What is the entropy change per cycle of the hot reservoir at 7 0 ∘ C ?

What is the entropy change per cycle of the cold reservoir?

Q12:

1.0 mol of an ideal gas is exactly tripled in volume by a reversible isothermal expansion in which the gas is heated by 1 3 0 0 J.

What is the change in entropy of the gas?

What is the temperature of the gas?

Q13:

A rock of mass 4.0 kg at a temperature of 2 3 ∘ C is dropped vertically downward a distance of 1 . 2 × 1 0 3 m into a shallow lake that is also at a temperature of 2 3 ∘ C .

What is the resulting change in the entropy of the universe?

If the temperature of the rock is 8 0 ∘ C when it is dropped, what is the change in the entropy of the universe? Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat of the lake’s water and use a value of 8 6 0 / ⋅ J k g C ∘ for the specific heat of the rock. Assume that the drag on the rock from the air is negligible.

Q14:

A pool of water of mass 40 g is at a temperature of 2 5 ∘ C . The water is heated until it becomes vapor at 1 0 0 ∘ C . Calculate the change in entropy of the water in this process. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water and use a value of 2 2 5 6 kJ/kg for the latent heat of vaporization of water.

Q15:

In an isochoric process, 5.0 mol of monatomic ideal gas at a temperature of 300 K is heated until its temperature reaches 370 K. What is the entropy change of the gas due to the heating?

Q16:

A pool of water of mass 60 g is at a temperature of 5 . 0 ∘ C . The water is heated by bringing it to thermal equilibrium with a reservoir at a temperature of 7 0 ∘ C . In calculating the entropy changes resulting from this process, use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water.

What is the entropy change of the reservoir due to the heating of the water?

What is the entropy change of the water due to the heating of the water?

What is the entropy change of the universe due to the heating of the water?

Q17:

A lump of ice at 0 . 0 ∘ C has a mass of 20 g. The ice is heated by the air, which is at a temperature negligibly greater than 0 . 0 ∘ C , until all of the ice melts. An identical lump of ice is heated by air at a temperature of 2 5 ∘ C . In determining the entropy changes resulting from these processes, use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water and use a value of 334 kJ/kg for the latent heat of fusion of ice.

What is the entropy change of the ice due to its melting by air at a temperature negligibly greater than 0 . 0 ∘ C ?

What is the entropy change of the air due to the ice’s melting at a temperature negligibly greater than 0 . 0 ∘ C ?

What is the entropy change of the universe due to the ice’s melting at a temperature negligibly greater than 0 . 0 ∘ C ?

What is the entropy change of the ice due to its melting by air at a temperature of 2 5 ∘ C ?

What is the entropy change of the air due to the ice’s melting at a temperature of 2 5 ∘ C ?

What is the entropy change of the universe due to the ice’s melting at a temperature of 2 5 ∘ C ?

Q18:

A 4.0 kg wood block starts with an initial speed of 9.0 m/s and slides across the floor until friction stops it. What is the approximate change in entropy of the universe? Assume that everything stays at a room temperature of 2 5 ∘ C .

Q19:

A glass beaker has a mass of 350 g. The beaker contains 450 g of water that is at a temperature of 2 5 ∘ C . The beaker is heated reversibly until the temperatures of both the beaker and the water are 6 0 ∘ C . Find the total change in entropy of the beaker and the water due to their heating. Use a value of 4 1 8 4 / ⋅ J k g C ∘ for the specific heat capacity of water and use a value of 8 4 0 / ⋅ J k g C ∘ for the specific heat capacity of glass.

Q20:

Suppose 25 g of ice at is added to 250 g of water at . Knowing that the latent heat of ice fusion is 334 kJ/kg and its specific heat is , what is the total change in entropy of the mixture after it reaches thermal equilibrium?

Q21:

A cylinder contains 600 g of helium at a pressure of 100 atm and a temperature of 2 5 . 0 ∘ C . The cylinder has a leaking valve and all the gas slowly escapes isothermally into the atmosphere. What is the change in entropy of the universe due to the leakage?

Q22:

Calculate the quality of steam at a pressure of 0.80 MPa and an entropy of 6.55 kJ/kg.

Q23:

Heat is added to a closed system to move the system from the state 𝑆 1 to the state 𝑆 2 . For 𝑆 1 , entropy = 𝑠 1 and temperature = 𝑇 1 . For 𝑆 2 , entropy = 𝑠 2 and temperature = 𝑇 2 . What is the net heating of the system in this process if 𝑇 = 𝑇 = 𝑇 1 2 ?

Q24:

What is the change in entropy when 1.0 kmol gas at a pressure of 1.0 MPa and a temperature of 300 K expands to a volume where it has a pressure 0.10 MPa? Assume that the expansion is isothermal.

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