Exercises: Temperature and heat

Aoife's bath is full of water at $38\ ^\circ\text{C}$ and on the kitchen table there is a cup of coffee at $70\ ^\circ\text{C}$. The scene is shown in the figure.

1. a) Which is at a higher temperature, the bathwater or the coffee?
2. b) Which of the two stores more thermal energy?
3. c) Explain in your own words the difference between temperature and heat.

The weather app on Cian's phone says that it is $14\ ^\circ\text{C}$ outside right now.

1. a) What quantity does a thermometer measure?
2. b) In which unit is temperature measured in Ireland?

Yesterday at twelve o'clock the school thermometer showed $9\ ^\circ\text{C}$ and today at the same time it shows $17\ ^\circ\text{C}$. How many degrees has the temperature risen?

Aitana puts a cold spoon into her bowl of very hot soup. Observe the figure.

1. a) Which object gives off heat and which receives it?
2. b) What happens to the temperatures of the soup and the spoon after a while?

To bathe his little brother, Álex mixes a saucepan of cold water with a saucepan of hot water. Is the mixture hotter than the hot water, colder than the cold water, or at an intermediate temperature? Explain your answer.

The school nurse takes Marc's temperature and the thermometer shows $37.8\ ^\circ\text{C}$. A temperature of $38\ ^\circ\text{C}$ or higher is considered a fever.

1. a) Does Marc have a fever?
2. b) How many tenths of a degree are missing to reach $38\ ^\circ\text{C}$?

Nadia drops an ice cube into a glass of soft drink that is at room temperature. Observe the figure.

1. a) Which body loses heat and which gains it?
2. b) How can this heat exchange be observed?

State whether the statement is true or false and correct the idea: "Heat and temperature are two names for the same thing."

In the kitchen you mix half a litre of water at $20\ ^\circ\text{C}$ with another half litre of water at $60\ ^\circ\text{C}$. Since there is the same amount of each, the final temperature is right in the middle. The diagram summarises the mixture.

1. a) Calculate the final temperature of the mixture.
2. b) Explain why it is neither $20\ ^\circ\text{C}$ nor $60\ ^\circ\text{C}$.

On Monday, the playground thermometer showed $4\ ^\circ\text{C}$ first thing in the morning and $13\ ^\circ\text{C}$ at midday.

1. a) How many degrees did the temperature rise in the morning?
2. b) If by night it fell by $10\ ^\circ\text{C}$ from midday, what temperature did the thermometer show then?

Aoife has prepared two pots of broth: a small one with $1\ \text{L}$ and a large one with $8\ \text{L}$, both at $90\ ^\circ\text{C}$. She removes them from the heat at the same time. Observe the figure.

1. a) Which of the two will cool down first?
2. b) Which of the two stored more thermal energy?
3. c) Reason your answers by separating the concepts of temperature and amount of energy.

The hot water from the tap at Omar's home comes out at $50\ ^\circ\text{C}$, which is too hot for taking a shower: he prefers it at $38\ ^\circ\text{C}$.

1. a) How many degrees does he want to lower the water temperature?
2. b) To achieve this, which tap should he turn up more, the cold or the hot water?
3. c) What happens to heat when the two streams of water mix?

Vera's sponge cake recipe says to preheat the oven to $180\ ^\circ\text{C}$. Once the oven is at that temperature, Vera puts in the baking tray with the batter, which was cold.

1. a) At first, which object transfers heat to which inside the oven?
2. b) Towards what temperature does the tray tend?
3. c) Can the tray become hotter than the oven? Justify your answer.

In a sports centre, the sauna is at $80\ ^\circ\text{C}$ and the changing room is at $24\ ^\circ\text{C}$.

1. a) How many degrees of difference are there between the two?
2. b) When you leave the sauna for the changing room, who loses heat, you or the air in the changing room? Explain your answer.

In the fireplace, an ember remains at $700\ ^\circ\text{C}$ and on the wall there is a radiator at $60\ ^\circ\text{C}$. However, the radiator heats the entire room, while the ember barely heats its immediate surroundings.

1. a) Which of the two is at a higher temperature?
2. b) Explain why the radiator heats more, considering its size.

On a summer afternoon, the pool water is at $24\ ^\circ\text{C}$ and the air is at $31\ ^\circ\text{C}$.

1. a) Who transfers heat to whom, the air to the water or the water to the air?
2. b) Which of the two will change temperature more slowly? Why?
3. c) If this situation lasted a very long time, what maximum temperature could the water reach?

Julia prepares warm water by mixing two glasses of cold water at $10\ ^\circ\text{C}$ with one glass of hot water at $70\ ^\circ\text{C}$. The diagram summarises the mixture.

1. a) Without calculating, will the final temperature be closer to $10\ ^\circ\text{C}$ or to $70\ ^\circ\text{C}$? Why?
2. b) When the amounts are not equal, the final temperature is a weighted average that takes into account how much of each water there is. Check it: add $2 \times 10 + 70$ and divide the result by $3$.
3. c) What are we assuming about the heat lost to the glass or to the air?

Youssef leaves a cup of milk at $80\ ^\circ\text{C}$ on the kitchen table, which is at $22\ ^\circ\text{C}$.

1. a) Describe how the temperature of the milk changes over time: does it drop as quickly at the beginning as when it is already warm?
2. b) If he waits a long time, what temperature will the milk reach?
3. c) Could the milk remain at $15\ ^\circ\text{C}$ in that kitchen? Justify your answer using the concept of thermal equilibrium.

The digital thermometer at Rayan's house takes half a minute to beep when taking his temperature under the armpit.

1. a) Explain, using the concept of thermal equilibrium, why it does not display the temperature instantly: what must happen between the armpit and the thermometer?
2. b) Why is it better for the thermometer to be small?
3. c) What would happen to the reading if you removed it before it beeped?

A documentary shows a giant iceberg at $0\ ^\circ\text{C}$ and, at home, a steaming cup of tea at $90\ ^\circ\text{C}$.

1. a) Which of the two has a higher temperature?
2. b) Which stores more thermal energy?
3. c) What needs to be known, besides temperature, to compare the energies of two objects? Use this example to explain the difference between heat and temperature.

Emma takes a can of soft drink out of the fridge, at $4\ ^\circ\text{C}$, and leaves it in the garden on a summer day when the air is at $32\ ^\circ\text{C}$.

1. a) What happens to the temperature of the can over time?
2. b) Roughly what temperature will it end up at?
3. c) Her cousin says that if she leaves it for many hours, it will reach $50\ ^\circ\text{C}$ "because it is very hot". Is he right? Justify your answer.

The heated towel rail in the bathroom is at $50\ ^\circ\text{C}$ and heats the whole bathroom; the flame of a match is at around $400\ ^\circ\text{C}$ and barely heats anything.

1. a) Which of the two has a higher temperature?
2. b) Which transfers more energy to its surroundings?
3. c) What two things must be taken into account to know how much heat an object can release?

The fridge does not "create cold": it removes heat from its interior and releases it outside through the grid at the back. Observe the diagram.

1. a) If you touch the rear grid of a running fridge, is it hot or cold?
2. b) Where does this heat come from?
3. c) Could you cool down the kitchen by leaving the fridge door open? Reason your answer by thinking about where the heat comes from and where it goes.

The school thermometer shows $35\ ^\circ\text{C}$ if we place it in the sun and $30\ ^\circ\text{C}$ if we place it in the shade, at the same time.

1. a) Which of the two readings better indicates the air temperature?
2. b) Why does the thermometer in the sun give a higher reading? Think about what the thermometer receives besides heat from the air.
3. c) Why do you think weather forecasts always give the temperature "in the shade"?