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The curve for unsteady state cooling or heating of bodies is
  • a)
    parabolic curve asymptotic to time axis
  • b)
    exponential curve asymptotic to time axis
  • c)
    exponential curve asymptotic both to time and temperature axes
  • d)
    hyperbolic curve asymptotic both to time and temperature axes
Correct answer is option 'B'. Can you explain this answer?
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Unsteady State Cooling or Heating Curve

The unsteady state cooling or heating of bodies is a phenomenon that occurs when a body is exposed to a temperature difference and the temperature of the body changes over time. The curve that represents this phenomenon is known as the unsteady state cooling or heating curve.

Exponential Curve

The unsteady state cooling or heating curve is an exponential curve asymptotic to the time axis. This means that as time passes, the temperature of the body approaches a final value, but never actually reaches it. The curve is characterized by a rapid decrease or increase in temperature at the beginning, followed by a slower approach to the final temperature.

Mathematical Representation

The unsteady state cooling or heating curve can be mathematically represented by the following equation:

ΔT = ΔT0 e^(-kt)

where ΔT is the change in temperature at time t, ΔT0 is the initial change in temperature, k is a constant depending on the properties of the body and the medium, and e is the mathematical constant approximately equal to 2.718.

Applications

The unsteady state cooling or heating curve has applications in various fields, including engineering, physics, and chemistry. It is used to model the cooling or heating of objects such as metals, liquids, and gases. The curve is also used in the design of cooling and heating systems, such as refrigeration and air conditioning systems, and in the optimization of thermal processes.
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