Question

At constant volume, 4 mol of an ideal gas when heated from 30 K to 500 K changes its internal energy by 5000 J.

The molar heat capacity at constant volume is:
a) 62.5 J/K
b) 1250 J/K
c) 250 J/K
d) 500 J/K

Answer 1

The change in internal energy for 4 moles of a monatomic ideal gas when heated from 30 K to 500 K is 5000 J. Consequently, the change in internal energy per degree Kelvin is approximately 10.64 J/K.

Step-by-step explanation:

The subject of this question is Physics, specifically the topic of heat capacities and internal energy change of an ideal gas. The grade level of this question is High School.

To determine the change in internal energy of an ideal gas at constant volume, we can use the formula ΔU = nCvΔT, where ΔU is the change in internal energy, n is the number of moles of gas, Cv is the molar heat capacity at constant volume, and ΔT is the change in temperature. For a monatomic ideal gas, the molar heat capacity at constant volume, Cv, is 3/2 R, where R is the universal gas constant (approximately 8.314 J/mol·K). Therefore, the change in internal energy for 4 moles of a monatomic ideal gas when heated from 30 K to 500 K is calculated as follows: ΔU = 4 mol * (3/2 * 8.314 J/mol·K) * (500 K - 30 K) = 4 * 3/2 * 8.314 * 470 = 5000 J.

Thus, the change in internal energy per degree Kelvin is ΔU/ΔT = 5000 J / 470 K = approximately 10.64 J/K.