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Heat and Thermodynamics question

2025 · 3 Apr · Shift 2 · Q65
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Heat and Thermodynamics question

2025 · 3 Apr · Shift 2 · Q65

JEE MainPhysicsHeat and ThermodynamicsMCQ+4 / −1
Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4%0.4 \%0.4% when heated by 1∘C1^{\circ} \mathrm{C}1∘C. Its initial temperature must be:
  1. A
    2500 K
  2. B
    25∘C25^{\circ} \mathrm{C}25∘C
  3. C
    250∘C250^{\circ} \mathrm{C}250∘C
  4. D
    250 K
View written solutionFree

Correct answer: D

  1. Use the ideal gas relation for a closed vessel

Since the gas is in a closed vessel, the volume is constant. For an ideal gas at constant volume,

P∝TP \propto TP∝T

so,

ΔPP=ΔTT\frac{\Delta P}{P} = \frac{\Delta T}{T}PΔP​=TΔT​

where TTT must be in kelvin.

  1. Convert the given percentage increase in pressure

Pressure increases by 0.4%0.4\%0.4% when heated by 1∘C1^\circ C1∘C.

Since a change of 1∘C1^\circ C1∘C equals a change of 1 K1\,K1K,

ΔPP=0.4%=0.4100=0.004\frac{\Delta P}{P} = 0.4\% = \frac{0.4}{100} = 0.004PΔP​=0.4%=1000.4​=0.004

and

ΔT=1 K\Delta T = 1\,KΔT=1K

  1. Apply the relation

Using

ΔPP=ΔTT\frac{\Delta P}{P} = \frac{\Delta T}{T}PΔP​=TΔT​

we get

0.004=1T0.004 = \frac{1}{T}0.004=T1​

So,

T=10.004=250 KT = \frac{1}{0.004} = 250\,KT=0.0041​=250K

  1. Match with the options

The initial temperature is

250 K\boxed{250\,K}250K​

So the correct option is D.

  1. Comparison with stored answer

Stored correct answer: D

Our derived answer: D

Hence, they agree.

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