Question

Question:You decide to take a nice hot bath but discover that your thoughtless roommate has used up most of the hot water. You fill the tub with 195 kg of 30.0°C water and attempt to warm it further by pouring in 5.00 kg of boiling water from the stove. (a) Is this a reversible or an irreversible process? Use physical reasoning to explain. (b) Calculate the final temperature of the bath water. (c) Calculate the net change in entropy of the system (bath water + boiling water), assuming no heat exchange with the air or the tub itself.

Short answer

The process is irreversible due to increase in entropy of the system.

Step-by-step solution

Identification of given data

The temperature of bath tub water is\({T_1} = 30\;^\circ {\rm{C}}\)

The temperature of boiling water is\({T_2} = 100\;^\circ {\rm{C}}\)

The mass of bath tub water is\({m_1} = 195\;{\rm{kg}}\)

The mass of boiling water is \({m_2} = 5\;{\rm{kg}}\)

Conceptual Explanation

The process is reversible and possible if the entropy of the system decreases otherwise process will be irreversible.

Whether the process is reversible or irreversible

The entropy of a system is the molecular disorder of molecules of the system. This disorder of the system is increased when the molecules are disturbed from its equilibrium state.

When the boiling water is poured into the bath tub water then there occurs disturbance in the molecules of boiling water and bath tub water due to the heat transfer between boiling water and bath tub water.

The molecular disorder of bathtub water increases in small amount due to huge amount of bathtub water. The molecular order of boiling water increases in large amount due to large decrease in its temperature. There is net increase in the entropy of the system so the process between bath tub water and boiling water is irreversible.

Therefore, the process is irreversible due to increase in entropy of the system.