Question

7 mol of a certain monoatomic ideal gas undergoes a temperature increase of 40 K at constant pressure. The increase in the internal energy of the gas in this process is:
(Given R = 8.3 JK^–1 mol^–1)

• A. 5810 J
• B. 3486 J
• C. 11620 J
• D. 6972 J

Answer 1

The Correct Option is B

To find the increase in internal energy of a monoatomic ideal gas, we need to use the specific relationship between the internal energy, temperature, and the degrees of freedom of the gas. The internal energy change for an ideal gas when it undergoes a temperature change is given by:

\Delta U = n \cdot C_v \cdot \Delta T

where:

• n is the number of moles of the gas.
• C_v is the molar heat capacity at constant volume for the gas.
• \Delta T is the change in temperature.

For a monoatomic ideal gas, the molar heat capacity at constant volume, C_v, is given by:

C_v = \frac{3}{2}R

Now, substituting the known values into the formula:

• n = 7 \, \text{mol}
• \Delta T = 40 \, \text{K}
• R = 8.3 \, \text{JK}^{-1}\text{mol}^{-1}

We can write:

\Delta U = 7 \cdot \left(\frac{3}{2} \cdot 8.3\right) \cdot 40

Calculate \Delta U :

• First, calculate \frac{3}{2} \cdot 8.3 = 12.45 \, \text{JK}^{-1}\text{mol}^{-1}
• Next, calculate \Delta U = 7 \cdot 12.45 \cdot 40 = 3486 \, \text{J}

Thus, the increase in the internal energy of the gas is 3486 J, which matches option (2).

Therefore, the correct answer is 3486 J.