Increase in Internal Energy of a Gas:

The internal energy of a gas is the sum of the kinetic energy and potential energy of its particles. When the temperature of a gas is increased, the average kinetic energy of its particles also increases. This leads to an increase in the internal energy of the gas.

Given Information:
- Temperature of one mole of helium gas is increased by 2.

To find:
- Increase in internal energy.

Solution:

The increase in internal energy can be calculated using the formula:

ΔU = nCΔT

Where:
ΔU is the increase in internal energy,
n is the number of moles of the gas,
C is the molar heat capacity of the gas at constant volume, and
ΔT is the change in temperature.

In this case, we are given that there is one mole of helium gas and the temperature is increased by 2.

Substituting the given values into the formula:

ΔU = 1 * C * 2

Since we are not given the molar heat capacity of helium at constant volume (C), we need to use the molar heat capacity of monatomic ideal gases at constant volume.

For monatomic ideal gases, the molar heat capacity at constant volume (Cv) is given by:

Cv = (3/2)R

Where R is the molar gas constant.

Substituting the value of Cv into the equation:

ΔU = 1 * (3/2)R * 2

Simplifying the equation:

ΔU = 3R

Since the molar gas constant (R) is approximately equal to 2 cal/mol·K, we can substitute this value into the equation:

ΔU = 3 * 2

ΔU = 6 cal

Therefore, the increase in internal energy of one mole of helium gas is 6 calories.

Answer: Option A) 6 cal