# Worksheet: Entropy Change in a Thermodynamic Process

In this worksheet, we will practice calculating the change in the entropy of a system that results from various thermodynamic processes.

**Q6: **

A 2.00 × 10^{2}-g mass of water at a temperature of is brought into thermal equilibrium successively with reservoirs at , , , and . Use a value of 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?

**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.

- A W/K
- B W/K
- C W/K
- D W/K
- E W/K

**Q9: **

A piece of aluminum of mass 0.50 kg is at a temperature of . The aluminum 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 aluminum.

**Q10: **

A mass of water of 200 g that has a temperature of is brought into contact with a heat reservoir at a temperature of , and thermal equilibrium is reached. Take the specific heat capacity of water to be .

What is the temperature of the water?

What is the temperature of the reservoir?

How much heat has been transferred in the process?

- A J
- B J
- C J
- D J
- E J

What is the entropy change of the water?

What is the entropy change of reservoir?

What is the entropy change of the universe?

**Q13: **

A rock of mass 4.0 kg at a temperature of is dropped vertically downward a distance of m into a shallow lake that is also at a temperature of .

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

If the temperature of the rock is when it is dropped, what is the change in the entropy of the universe? Use a value of for the specific heat of the lake’s water and use a value of 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 . The water is heated until it becomes vapor at . Calculate the change in entropy of the water in this process. Use a value of for the specific heat capacity of water and use a value of 2,256 kJ/kg for the latent heat of vaporization of water.

**Q16: **

A pool of water of mass 60 g is at a temperature of . The water is heated by bringing it to thermal equilibrium with a reservoir at a temperature of . In calculating the entropy changes resulting from this process, use a value of 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 has a mass of 20 g. The ice is heated by the air, which is at a temperature negligibly greater than , until all of the ice melts. An identical lump of ice is heated by air at a temperature of . In determining the entropy changes resulting from these processes, use a value of 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 ?

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

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

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

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

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

**Q19: **

A glass beaker has a mass of 350 g. The beaker contains 450 g of water that is at a temperature of . The beaker is heated reversibly until the temperatures of both the beaker and the water are . Find the total change in entropy of the beaker and the water due to their heating. Use a value of for the specific heat capacity of water and use a value of for the specific heat capacity of glass.

**Q20: **

Suppose 25 g of ice at a temperature of is added to 250 g of water at a temperature of . Using a value for the latent heat of fusion of ice of 334 kJ/kg and using a value of the specific heat capacity of ice of , find the total change in entropy of the mixture after it reaches thermal equilibrium.

**Q25: **

A gas is heated isothermally by 25 kJ at a temperature of 350 K. How much does the gas increase in entropy? Answer to three significant figures.