#### To determine

**To sketch:** The possible graph of *T* as a function of time *t* that has elapsed since the faucet was turned on.

#### Explanation

**Fact:**

Since temperature *T* is proportional to the time *t* up to which the faucet has been running.

That is, T∝t which implies T=kt+c, where *k* and *c* are constants.

Since at the starting the process the water is present in the pipes whose temperature is same as the room temperature which implies the initial temperature of water in the faucet is nearly equal to the room temperature. After sometime, the hot water comes out as *T* starts increasing.

Again in the next time phase the temperature of the water coming out becomes stable

without any fluctuation. Slowly, the temperature decreases as the heat energy of the water

is lost to the environment.

Use the above information and draw the possible graph of Temperature versus time as shown in Figure 1.

#### To determine

**To describe:** The rate of change of *T* with respect to the time *t* varies as *t* increases.

#### Explanation

Since temperature *T* is proportional to the time *t* up to which the faucet has been running.

That is, T∝t which implies T=kt+c, where *k* and *c* are constants.

So, the temperature will increase linearly.

The initial temperature of water in the faucet is nearly equal to the room temperature.

After sometime, the hot water comes out as *T* starts increasing which means that dTdt>0.

Again in the next time phase the temperature of the water coming out becomes stable

without any fluctuation which means that dTdt≈0. Slowly, the temperature decreases which means that dTdt<0.

#### To determine

**To sketch:** The graph of dTdt versus *t* graph.

#### Explanation

Use the information in part (b) and draw the graph of dTdt versus time as shown

in Figure 2.

From Figure 2, it is observed that initially the rate of change of temperature is positive which becomes zero and then becomes negative.