# 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.

Phiên bản tương tác: https://www.calcopenly.com/vi/science/heat-transfer-calculator
Chủ đề: Máy tính khoa học theo chủ đề

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.

## Dữ liệu đầu vào

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

## Kết quả

- Heat (J) — kết quả chính
- Khối lượng (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

## Công thức

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

## Ví dụ có lời giải

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

- Calculate: Temperature change
- Solve for: Heat
- Material: Water (liquid, 15 °C)
- Khối lượng: 1 kg
- Initial temperature: 20 °C
- Final temperature: 100 °C
- **Heat: 334,880 J**
- **Heat: 0.093022 kWh**
- Nguồn đối chiếu: 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)
- Khối lượng: 1 kg
- Initial temperature: 80 °C
- Final temperature: 20 °C
- **Heat: -251,160 J**
- Nguồn đối chiếu: 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
- Khối lượng: 500 g
- Initial temperature: 20 °C
- **Final temperature: 40 °C**
- **Temperature change: 20 K**
- Nguồn đối chiếu: 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
- Khối lượng: 1 kg
- Initial temperature: 20 °C
- Final temperature: 30 °C
- **Specific heat capacity: 387 J/(kg·K)**
- Nguồn đối chiếu: Python 3.8: 3870/(1 × 10) = 387 J/(kg·K), copper in OpenStax Table 1.3

### Melt 2 kg of ice

- Calculate: Phase change
- Khối lượng: 2 kg
- Solve for: Heat
- Substance: Water
- Change: Melting / freezing
- **Heat: 668,000 J**
- Nguồn đối chiếu: Python 3.8: 2 × 334 kJ/kg (OpenStax Table 1.4)

### Boil away 500 g of water

- Calculate: Phase change
- Khối lượng: 0.5 kg
- Solve for: Heat
- Substance: Water
- Change: Boiling / condensing
- **Heat: 1,128,000 J**
- Nguồn đối chiếu: Python 3.8: 0.5 × 2256 kJ/kg (OpenStax Table 1.4)

## Câu hỏi

### 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.

### “Specific heat, latent heat and Carnot efficiency calculator” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 10. Ví dụ, “Heat 1 kg of water from 20 °C to 100 °C” được kiểm tra bằng Python 3.8 fractions: 1 × 4186 × 80 = 334880 J (OpenStax c_water = 4186).

### Phương pháp này lấy từ đâu?

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.

## Nguồn

- [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)