The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T1K to T2K is (a) 3/4Na kB (T₂ - T₁) (b) 3/4Na kB ((T₂)/(T₁)) (c) 3/8Na kB (T₂ - T₁) (d) 3/2Na kB (T₂ - T₁)

Answer: (c). Helium is monoatomic: CV = 3/2R; 1 g He is n = 1/4 mol. Q = nCVΔ T = 1/4 × 3/2R(T₂ - T₁) = 3/8R(T₂ - T₁) With R = Na kB: Q = 3/8Na kB (T₂ - T₁) So the answer is (c).

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Q77NEET 2013Medium

Gas Laws & Ideal Gas Equation

The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from T1K to T2K is

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Answer: (c)

Helium is monoatomic: $C_V = \dfrac{3}{2}R$ ; 1 g He is $n = \dfrac{1}{4}$ mol.
$Q = nC_V\Delta T = \dfrac{1}{4} \times \dfrac{3}{2}R(T_2 - T_1) = \dfrac{3}{8}R(T_2 - T_1)$
With $R = N_a k_B$ : $Q = \dfrac{3}{8}N_a k_B (T_2 - T_1)$
So the answer is (c).

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