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The specific heat c of a solid at low temperature shows temperature dependence according to the relation c = DT3 where D is a constant and T is the temperature in kelvin. A piece of this solid of mass m kg is taken and its temperature is raised from 20 K to 30 K. The amount of the heat required in the process in energy units is
  • a)
    5 × 104 Dm
  • b)
    (33/4) × 104 Dm
  • c)
    (65/4) × 104 Dm
  • d)
    (5/4) × 104 Dm
Correct answer is option 'C'. Can you explain this answer?
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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).
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The specific heat c of a solid at low temperature shows temperature dependence according to the relation c = DT3 where D is a constant and T is the temperature in kelvin. A piece of this solid of mass m kg is taken and its temperature is raised from 20 K to 30 K. The amount of the heat required in the process in energy units isa)5 × 104 Dmb)(33/4) × 104 Dmc)(65/4) × 104 Dmd)(5/4) × 104 DmCorrect answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The specific heat c of a solid at low temperature shows temperature dependence according to the relation c = DT3 where D is a constant and T is the temperature in kelvin. A piece of this solid of mass m kg is taken and its temperature is raised from 20 K to 30 K. The amount of the heat required in the process in energy units isa)5 × 104 Dmb)(33/4) × 104 Dmc)(65/4) × 104 Dmd)(5/4) × 104 DmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The specific heat c of a solid at low temperature shows temperature dependence according to the relation c = DT3 where D is a constant and T is the temperature in kelvin. A piece of this solid of mass m kg is taken and its temperature is raised from 20 K to 30 K. The amount of the heat required in the process in energy units isa)5 × 104 Dmb)(33/4) × 104 Dmc)(65/4) × 104 Dmd)(5/4) × 104 DmCorrect answer is option 'C'. Can you explain this answer?.
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