The specific heat c of a solid at low temperature shows temperature de...
The specific heat c of a solid at low temperature shows temperature de...
Given Data:
- Specific heat of the solid: c = DT^3
- Temperature range: 20 K to 30 K
- Mass of the solid: m kg
Calculating Heat Required:
- The heat required to raise the temperature of the solid can be calculated using the formula Q = mcΔT, where Q is the heat energy, m is the mass, c is the specific heat, and ΔT is the change in temperature.
- Substituting the given specific heat equation c = DT^3 into the formula, we get Q = mDT^3ΔT
- The change in temperature ΔT = 30 K - 20 K = 10 K
- Substituting the values, we get Q = mD(30^3 - 20^3)
Solving for the Heat Required:
- Q = mD(27,000 - 8,000)
- Q = 19,000mD
- Q = 19 × 10^3Dm
Answer:
- Therefore, the amount of heat required in the process is 19 × 10^3Dm or 19,000Dm energy units.
- Option (c) (65/4) × 10^4 Dm is equivalent to 19,000Dm, hence the correct answer is option (c).