How much energy would it require to heat 20 grams of ice at -20°C to steam at [Free] B117
How much energy would it require to heat 20 grams of ice at -20°C to steam at 120°C ? Do the m ,[ice =0.5calgm
Answer
Thermodynamic Analysis: From Ice at -20°C to Steam at 120°C
This comprehensive analysis walks through the detailed thermodynamic process of converting 20 grams of ice at -20°C into steam at 120°C. It includes phase transitions (solid → liquid → gas) and calculations for energy input using fundamental principles of heat transfer and thermodynamics.
Step 1: Heating Ice from -20°C to 0°C
To raise the temperature of ice from -20°C to 0°C, we apply the specific heat of ice, which is 0.5 cal/g°C.
Energy required: 200 calories
Step 2: Melting Ice at 0°C
The phase change from ice to water at 0°C requires latent heat of fusion. For ice, it is 80 cal/g.
Energy required: 1600 calories
Step 3: Heating Water from 0°C to 100°C
Now, the water must be heated from 0°C to its boiling point at 100°C. The specific heat of water is 1 cal/g°C.
Energy required: 2000 calories
Step 4: Vaporizing Water at 100°C
The conversion of water to steam at 100°C requires the latent heat of vaporization, which is 540 cal/g.
Energy required: 10800 calories
Step 5: Heating Steam from 100°C to 120°C
The steam is then heated from 100°C to 120°C using the specific heat of steam, 0.5 cal/g°C.
Energy required: 200 calories
Total Energy Required
Summing all the heat energy from each step gives:
| Step | Transition | Formula Used | Energy (cal) |
|---|---|---|---|
| 1 | Heating ice (-20°C to 0°C) | Q = mcΔT | 200 |
| 2 | Melting ice | Q = mL (fusion) | 1600 |
| 3 | Heating water (0°C to 100°C) | Q = mcΔT | 2000 |
| 4 | Vaporizing water | Q = mL (vaporization) | 10800 |
| 5 | Heating steam (100°C to 120°C) | Q = mcΔT | 200 |
| Total | 14,800 | ||
Thermodynamic Concepts Explained
- Specific Heat: Energy required to raise temperature of 1g of substance by 1°C.
- Latent Heat: Energy absorbed/released during phase change without temperature change.
- Phase Transition: Occurs at constant temperature but requires significant energy.
- Heat Addition: Depends on mass, specific heat, and temperature change.
Conclusion
To completely convert 20 grams of ice at -20°C into steam at 120°C, a total of 14,800 calories is required. This energy spans across five thermal processes, each critical in understanding the fundamentals of thermodynamics. From specific heats to latent heats, the concepts demonstrated here form a strong foundation for further exploration in physics and energy science.