What is the total internal energy of 2.4 mol of an ideal gas which has a temperature of 15 °C? - AQA - A-Level Physics - Question 11 - 2017 - Paper 2

The total internal energy (U) of an ideal gas can be calculated using the formula:

$U = nC_vT$

where:

• $n$ = number of moles = 2.4 mol
• $C_v$ = molar specific heat capacity at constant volume for a monatomic ideal gas = ( \frac{3R}{2} ), where ( R ) is the universal gas constant, approximately ( 8.314 , \text{J/(mol K)} ).
• $T$ = temperature in Kelvin = 15 °C + 273.15 = 288.15 K.

Now, substituting the values into the formula:

1. Convert ( C_v ): $C_v = \frac{3 \times 8.314}{2} = 12.471 \, \text{J/(mol K)}$

2. Now, calculate the internal energy: $U = 2.4 \, \text{mol} \times 12.471 \, \text{J/(mol K)} \times 288.15 \, ext{K}$

3. Therefore, $U \approx 2.4 \times 12.471 \times 288.15 \approx 8.6 \times 10^3 \, ext{J}$

Hence, the total internal energy is approximately ( 8.6 \times 10^3 , ext{J} ).