# Specific heat, latent heat and Carnot efficiency calculator

> Heat energy from Q = mcΔT (solve for heat, mass, final temperature or specific heat), latent heat Q = mL for melting or boiling, and Carnot efficiency.

Versione interattiva: https://www.calcopenly.com/it/science/heat-transfer-calculator
Argomento: Calcolatori scientifici

Warming or cooling a material takes heat Q = mcΔT, where m is the mass, c the specific heat capacity and ΔT the temperature change; the calculator solves for any one of heat, mass, final temperature or specific heat. Melting or boiling takes Q = mL at constant temperature, where L is the latent heat. The Carnot mode gives the upper limit on any heat engine's efficiency, 1 − Tc/Th with both temperatures in kelvin.

The default, 1 kg of water heated from 20 °C to 100 °C, needs 334,880 J (0.093 kWh), what a 2 kW kettle delivers in 2 minutes 47 seconds with no losses. Boiling that water away takes a further 2,256 kJ, almost seven times as much.

Specific heats are room-temperature values from OpenStax University Physics (Table 1.3). In reality c varies with temperature, and the calculation assumes no melting or boiling between the two temperatures.

## Dati

- **Calculate** (opzioni: Temperature change, Phase change, Carnot efficiency)
- **Solve for** (opzioni: Heat, Massa, Final temperature, Specific heat)
- **Material** (opzioni: Water (liquid, 15 °C), Ice (average −50 to 0 °C), Aluminium, Copper, Iron / steel, Lead, Silver, Gold, Glass, Concrete / granite, Legno, Ethanol, Mercury, Human body (average), Enter specific heat)
- **Specific heat capacity**
- **Heat added (negative if removed)**
- **Massa**
- **Initial temperature**
- **Final temperature**
- **Solve for** (opzioni: Heat, Massa)
- **Substance** (opzioni: Water, Ethanol, Nitrogen, Lead, Enter latent heat)
- **Change** (opzioni: Melting / freezing, Boiling / condensing)
- **Latent heat**
- **Show heat in** (opzioni: J, kJ, kcal, BTU)
- **Show temperatures in** (opzioni: °C, °F, K)
- **Hot reservoir temperature**
- **Cold reservoir temperature**
- **Heat taken from the hot side**

## Risultati

- Heat (J) — risultato principale
- Massa (kg)
- Final temperature (°C)
- Specific heat capacity (J/(kg·K))
- Temperature change (K)
- Heat (kWh)
- Carnot efficiency
- Maximum work from that heat (J)
- Best refrigerator COP
- Best heat-pump COP

## Formula

$$
Q = mc\Delta T,\qquad Q = mL,\qquad \eta_{\text{Carnot}} = 1 - \frac{T_C}{T_H}
$$

## Esempi svolti

### Heat 1 kg of water from 20 °C to 100 °C

- Calculate: Temperature change
- Solve for: Heat
- Material: Water (liquid, 15 °C)
- Massa: 1 kg
- Initial temperature: 20 °C
- Final temperature: 100 °C
- **Heat: 334,880 J**
- **Heat: 0.093022 kWh**
- Fonte di verifica: Python 3.8 fractions: 1 × 4186 × 80 = 334880 J (OpenStax c_water = 4186)

### Cooling releases heat (negative Q)

- Calculate: Temperature change
- Solve for: Heat
- Material: Water (liquid, 15 °C)
- Massa: 1 kg
- Initial temperature: 80 °C
- Final temperature: 20 °C
- **Heat: -251,160 J**
- Fonte di verifica: Python 3.8: 1 × 4186 × (20 − 80)

### 9 kJ into 500 g of aluminium at 20 °C

- Calculate: Temperature change
- Solve for: Final temperature
- Material: Aluminium
- Heat added (negative if removed): 9 kJ
- Massa: 500 g
- Initial temperature: 20 °C
- **Final temperature: 40 °C**
- **Temperature change: 20 K**
- Fonte di verifica: Python 3.8 fractions: ΔT = 9000/(0.5 × 900) = 20 K

### Identify a metal: 3870 J warms 1 kg by 10 K

- Calculate: Temperature change
- Solve for: Specific heat
- Heat added (negative if removed): 3870 J
- Massa: 1 kg
- Initial temperature: 20 °C
- Final temperature: 30 °C
- **Specific heat capacity: 387 J/(kg·K)**
- Fonte di verifica: Python 3.8: 3870/(1 × 10) = 387 J/(kg·K), copper in OpenStax Table 1.3

### Melt 2 kg of ice

- Calculate: Phase change
- Massa: 2 kg
- Solve for: Heat
- Substance: Water
- Change: Melting / freezing
- **Heat: 668,000 J**
- Fonte di verifica: Python 3.8: 2 × 334 kJ/kg (OpenStax Table 1.4)

### Boil away 500 g of water

- Calculate: Phase change
- Massa: 0.5 kg
- Solve for: Heat
- Substance: Water
- Change: Boiling / condensing
- **Heat: 1,128,000 J**
- Fonte di verifica: Python 3.8: 0.5 × 2256 kJ/kg (OpenStax Table 1.4)

## Domande

### How much energy does it take to heat water?

4,186 J per kilogram per degree Celsius, water's specific heat capacity. Heating 1 litre (1 kg) from 20 °C to 100 °C takes 1 × 4,186 × 80 = 334,880 J, or 0.093 kWh. In US units that is about 1 BTU per pound per °F, which is how the BTU was originally defined.

### What is specific heat capacity?

The heat needed to raise 1 kg of a substance by 1 K (the same as 1 °C), in J/(kg·K). Water's is 4,186, among the highest of common substances, while copper's is 387 and lead's 128. The same 10 kJ warms 1 kg of water by 2.4 °C but 1 kg of copper by 25.8 °C, which is why water is used for cooling and heat storage.

### What is latent heat?

The energy absorbed or released during a phase change at constant temperature, Q = mL. For water the latent heat of fusion is 334 kJ/kg at 0 °C and of vaporisation 2,256 kJ/kg at 100 °C (OpenStax Table 1.4). Melting 2 kg of ice takes 668 kJ, enough to heat the same 2 kg of water by about 80 °C.

### What is the Carnot efficiency?

η = 1 − Tc/Th, the largest fraction of heat that any engine can turn into work between a hot reservoir at Th and a cold one at Tc, both in kelvin. Between 500 K and 300 K it is 40%; between boiling and freezing water, 26.8%. Real engines fall short of it: coal-fired power stations typically convert about 37% of their fuel's heat into electricity.

### What is the maximum COP of a heat pump?

COP = Th/(Th − Tc) with temperatures in kelvin, the Carnot limit on heat delivered per unit of work. Pumping heat from 0 °C outdoors into a 35 °C heating loop allows at most 308.15/35 ≈ 8.8. At −10 °C outside the limit drops to 6.8, and real machines stay well below it because of compressor and heat-exchanger losses.

### Quanto è preciso «Specific heat, latent heat and Carnot efficiency calculator»?

La precisione dipende dai dati inseriti e dalle ipotesi del metodo. Il calcolo decimale usa 50 cifre significative, ma stime, metodi numerici e dati di origine possono essere meno precisi; l’arrotondamento visualizzato non elimina questi limiti. Esempi svolti verificati con fonti indipendenti: 10. Per esempio, «Heat 1 kg of water from 20 °C to 100 °C» viene verificato con Python 3.8 fractions: 1 × 4186 × 80 = 334880 J (OpenStax c_water = 4186).

### Da dove proviene il metodo?

OpenStax University Physics Volume 2, §1.5 Heat transfer, specific heat and calorimetry (Table 1.3); §1.6 Phase changes (Table 1.4); OpenStax University Physics Volume 2, §4.5 The Carnot cycle.

## Fonti

- [OpenStax University Physics Volume 2, §1.5 Heat transfer, specific heat and calorimetry (Table 1.3); §1.6 Phase changes (Table 1.4)](https://openstax.org/books/university-physics-volume-2/pages/1-5-heat-transfer-specific-heat-and-calorimetry)
- [OpenStax University Physics Volume 2, §4.5 The Carnot cycle](https://openstax.org/books/university-physics-volume-2/pages/4-5-the-carnot-cycle)