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NEET PHYSICSKinetic TheoryMedium

Question

The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T1T_1 K to T2T_2 K is:

A

32NakB(T2T1)\frac{3}{2} N_a k_B (T_2 - T_1)

B

34NakB(T2T1)\frac{3}{4} N_a k_B (T_2 - T_1)

C

34NakBT2T1\frac{3}{4} N_a k_B \frac{T_2}{T_1}

D

38NakB(T2T1)\frac{3}{8} N_a k_B (T_2 - T_1)

Step-by-Step Solution

  1. Identify the Gas and Moles: Helium (He) is a monoatomic gas. Its molar mass (MM) is 4 g/mol4 \text{ g/mol}. Given mass m=1 gm = 1 \text{ g}. Number of moles n=mM=14 moln = \frac{m}{M} = \frac{1}{4} \text{ mol}.
  2. Identify Specific Heat: For a monoatomic gas, the molar specific heat at constant volume is Cv=32RC_v = \frac{3}{2}R. (Note: While the problem mentions NTP, which often implies constant pressure, the available options match the calculation for constant volume or internal energy change. If calculated at constant pressure, Cp=52RC_p = \frac{5}{2}R, yielding a coefficient of 5/8, which is not an option).
  3. Calculate Heat Energy: The heat energy required (QQ) is given by Q=nCvΔTQ = n C_v \Delta T. Q=(14)×(32R)×(T2T1)=38R(T2T1)Q = \left(\frac{1}{4}\right) \times \left(\frac{3}{2}R\right) \times (T_2 - T_1) = \frac{3}{8} R (T_2 - T_1).
  4. Substitute Constants: The universal gas constant RR is related to the Boltzmann constant (kBk_B) and Avogadro's number (NaN_a) by the equation R=NakBR = N_a k_B. Substituting this into the heat equation: Q=38NakB(T2T1)Q = \frac{3}{8} N_a k_B (T_2 - T_1).
  5. Correction Note: The input text '111 g' is interpreted as a typo for '1 g' based on the mathematical derivation yielding the correct option.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from Kinetic Theory. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSKinetic Theoryamountenergyrequiredtemperaturehelium

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