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NEET
Exam
NEET
Subject
Physics
Chapter
Thermal Properties of Matter

NEET · Physics · Thermal Properties of Matter

Two identical beakers A and B contain equal volumes of two...

Two identical beakers AA and BB contain equal volumes of two different liquids at 60°C60 ° C each and left to cool down. Liquid in AA has density of 8×102kgm−38 \times {10}^{2}kg{m}^{- 3} and specific heat of 2000Jkg−1K−12000Jk{g}^{- 1}{K}^{- 1} while the liquid in BB has density 103kgm−3{10}^{3}kg{m}^{- 3} and specific heat of 4000Jkg−1K−14000Jk{g}^{- 1}{K}^{- 1}. Which of the following best describes their temperature versus time graph schematically? (assume the emissivity of both the beakers to be the same)Two identical beakers A and B contain equal volumes of two different liquids at 60 ° C each and left to cool down.Two identical beakers A and B contain equal volumes of two different liquids at 60 ° C each and left to cool down.Two identical beakers A and B contain equal volumes of two different liquids at 60 ° C each and left to cool down.Two identical beakers A and B contain equal volumes of two different liquids at 60 ° C each and left to cool down.

Options

  1. ASTATEMENT-I:In SHM let x be the maximum speed, y the frequency of oscillation and z the maximum acceleration, then (((x
  2. BSTATEMENT-I:In SHM let x be the maximum speed, y the frequency of oscillation and z the maximum acceleration, then (((x
  3. CSTATEMENT-I:In SHM let x be the maximum speed, y the frequency of oscillation and z the maximum acceleration, then (((x
  4. DSTATEMENT-I:In SHM let x be the maximum speed, y the frequency of oscillation and z the maximum acceleration, then (((x

Correct answer

B. STATEMENT-I:In SHM let x be the maximum speed, y the frequency of oscillation and z the maximum acceleration, then (((x

Step-by-step solution

From Newton's law of cooling,
Rate of cooling: (−dTdt)=4\sigmaeAT03(T−T0)ms∝1ms\left(- \dfrac{dT}{dt}\right) = \dfrac{4\sigmaeA{T}_{0}^{3}\left(T - {T}_{0}\right)}{ms}∝ \dfrac{1}{ms}
∴ρA<ρB∴ {ρ}_{A} < {ρ}_{B}
mA<mB{m}_{A} < {m}_{B}
And sA<sB{s}_{A} < {s}_{B}
mAsA<mBsB{m}_{A}{s}_{A} < {m}_{B}{s}_{B}
At t=0,(−dTdt)A>(−dTdt)Bt = 0, {\left(- \dfrac{dT}{dt}\right)}_{A} > {\left(- \dfrac{dT}{dt}\right)}_{B}
Initially, the rate of cooling for AA will be higher than BB and temperature (T)( T ) vs time (t)( t ) graph will be a curve.
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