Question

Initial volume of 1 mole of a monoatomic gas is 2 litres. It is expanded isothermally to a volume of 6 litres. Change in internal energy is xR. Find x.

Answer 1

Correct Answer: 0

To determine the change in internal energy for the isothermal expansion of a monoatomic gas, we start by noting that for an isothermal process, the temperature remains constant. According to the first law of thermodynamics, the change in internal energy (ΔU) for an ideal gas during an isothermal process is zero because internal energy depends solely on temperature, and there's no change in temperature. For any isothermal process, particularly of an ideal gas, the internal energy change is expressed as:

ΔU = n * Cv * ΔT

Where,

• n = number of moles of gas
• Cv = molar heat capacity at constant volume
• ΔT = change in temperature

Since ΔT = 0 for an isothermal process, we have:

• ΔU = n * Cv * 0 = 0

Thus, ΔU = 0 for the given process.

Given in the question, this change, ΔU, is expressed as xR where x = ΔU/R and since ΔU = 0:

• x = 0/R = 0

Therefore, the value of x is 0, which neatly fits the expected range of 0,0 specified in the problem statement.