The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from $T_1K$ to $T_2K$ is

Question

In a Vernier caliper, $N+1$ divisions of vernier scale coincide with $N$ divisions of main scale. If 1 MSD represents 0.1 mm, the vernier constant (in cm) is:

Answer 1

To determine the amount of heat energy required to raise the temperature of 1 g of Helium from $ T_1 $ K to $ T_2 $ K at NTP (Normal Temperature and Pressure), we'll use the concepts of specific heat capacity and molar heat capacity.

Helium is a monoatomic ideal gas, and its molar heat capacity at constant volume, $ C_V $, is given by:

C_V = \frac{3}{2}R

where $ R $ is the universal gas constant.

First, let's convert 1 g of Helium to moles. The molar mass of Helium (He) is 4 g/mol, thus:

\text{Number of moles of He} = \frac{1}{4} \, \text{mol}

The heat required, $ Q $, to increase the temperature from $ T_1 $ to $ T_2 $ is given by:

Q = n \cdot C_V \cdot (T_2 - T_1)

Substitute the values:

Q = \left(\frac{1}{4}\right) \times \left(\frac{3}{2} R \right) \times (T_2 - T_1)

Simplifying further:

Q = \frac{3}{8} R (T_2 - T_1)

Since $ R = N_a K_B $, where $ N_a $ is Avogadro's number and $ K_B $ is the Boltzmann constant:

Q = \frac{3}{8} N_a K_B (T_2 - T_1)

Thus, the amount of heat energy required is:

The correct answer is \frac3{8} N_a K_B (T_2 - T_1).

This result matches the given correct answer, confirming that the calculation is accurate.

Answer 2