# The Calorimetry Detective

![Figure 1: Clean labelled diagram in the style of a textbook figure illustrating Enthalpy changes and calorimetry: the equipment, materials and key](https://goa-cc-uat-aili-app-001.azurewebsites.net/api/generate/b6eb916a-7607-4563-9475-ef9765b3bfb8/asset/436)

This puzzle challenges you to apply the heat transfer equation Q = mcΔt and interpret enthalpy data from a calorimetry experiment ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23634), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23641)). You will determine energy changes in chemical reactions by working backwards from thermal measurements ([Topic](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23633)).

## The puzzle

A student burns a food sample in a calorimeter. The calorimeter contains 200 grams of water. Before the reaction, the water temperature is 22°C. After the reaction, the water temperature rises to 38°C.

The student then repeats the experiment with a different food sample of the same mass. This time the water temperature rises from 22°C to 45°C.

The specific heat capacity of water is 4.18 J/(g·°C).

**Your task:** Calculate the heat released by each food sample. Then determine which sample released more energy per gram of food burned, and by how much (in joules).

## Hints

**Hint 1:** Use the equation Q = mcΔt for each trial. Remember that ΔT is the change in temperature, not the final temperature.

**Hint 2:** The mass of water is the same in both trials. The specific heat capacity is the same. Only the temperature change differs between the two experiments.

**Hint 3:** Once you have calculated Q for each sample, compare the two values. The difference between them is the additional energy released by the second sample.

## Answer key

**First sample:**
ΔT = 38°C − 22°C = 16°C
Q = mcΔt = 200 g × 4.18 J/(g·°C) × 16°C = 13,376 J

**Second sample:**
ΔT = 45°C − 22°C = 23°C
Q = mcΔt = 200 g × 4.18 J/(g·°C) × 23°C = 19,228 J

**Difference:**
19,228 J − 13,376 J = 5,852 J

The second food sample released 5,852 joules more energy than the first sample.

**Reasoning:** Calorimetry measures the heat transferred from a chemical reaction to the surroundings (the water). The larger the temperature change in the water, the more heat was released by the reaction. By applying Q = mcΔt to both trials and comparing the results, you determine that the second food sample is a more energy-dense fuel ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23634), [Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23641)). This type of calculation is central to determining enthalpy changes from experimental data ([Outcome](https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23638)).

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*AILI game · language en · model claude-haiku-4-5-20251001 · generated 2026-09-17 · id b6eb916a-7607-4563-9475-ef9765b3bfb8*

### Sources

- node:n1: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes › General Outcome 1 (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23636)
- node:n2: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes › General Outcome 1 (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23634)
- node:n3: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes › General Outcome 1 (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23641)
- node:n4: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes › General Outcome 1 (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23634)
- node:n5: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes › General Outcome 1 (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23636)
- node:n6: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes › General Outcome 1 (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23638)
- resource:r1: Resources › type#studentsupport, type#teachersupport › SCN3796 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/YlIUl7k3G0y6R-b8XyPAGw)
- node:n7: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes › General Outcome 1 (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23648)
- resource:r2: Resources › type#activity › SCN3796 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/9ykNTynh306g6EnZlkTITQ)
- node:n8: Chemistry › Chemistry (20, 30) › Chemistry 30 › Unit A: Thermochemical Changes (https://goa-cc-uat-aili-app-001.azurewebsites.net/explore/node/23633)
- resource:r3: Resources › type#activity › SCN3796 (https://goa-cc-uat-aili-app-001.azurewebsites.net/library/resource/0uxhxD914kqzmssVwCK4tg)