Solved: PHYSICS Question for NEET

NEET PHYSICSMedium

The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from $T_1$ K to $T_2$ K is:

$\frac{3}{2} N_a k_B (T_2 - T_1)$

$\frac{3}{4} N_a k_B (T_2 - T_1)$

$\frac{3}{4} N_a k_B \frac{T_2}{T_1}$

$\frac{3}{8} N_a k_B (T_2 - T_1)$

Identify the Gas and Moles: Helium (He) is a monoatomic gas. Its molar mass ( $M$ ) is $4 \text{ g/mol}$ . Given mass $m = 1 \text{ g}$ . Number of moles $n = \frac{m}{M} = \frac{1}{4} \text{ mol}$ .
Identify Specific Heat: For a monoatomic gas, the molar specific heat at constant volume is $C_v = \frac{3}{2}R$ . (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, $C_p = \frac{5}{2}R$ , yielding a coefficient of 5/8, which is not an option).
Calculate Heat Energy: The heat energy required ( $Q$ ) is given by $Q = n C_v \Delta T$ . $Q = \left(\frac{1}{4}\right) \times \left(\frac{3}{2}R\right) \times (T_2 - T_1) = \frac{3}{8} R (T_2 - T_1)$ .
Substitute Constants: The universal gas constant $R$ is related to the Boltzmann constant ( $k_B$ ) and Avogadro's number ( $N_a$ ) by the equation $R = N_a k_B$ . Substituting this into the heat equation: $Q = \frac{3}{8} N_a k_B (T_2 - T_1)$ .
Correction Note: The input text '111 g' is interpreted as a typo for '1 g' based on the mathematical derivation yielding the correct option.

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