1 mol sample of an ideal gas is kept at 0°C during an expansion from 13.0 to 20.0L.how much energy transfer by heat occurs between gas and its surroundings in KJ

To determine the energy transfer by heat during the expansion of an ideal gas, we can use the principles of thermodynamics. In this case, since the gas is expanding at a constant temperature (isothermal process), we can apply the ideal gas law and the formula for heat transfer in isothermal conditions.

Understanding the Isothermal Expansion

In an isothermal process, the temperature of the gas remains constant. For an ideal gas, this means that any work done by the gas during expansion must be compensated by heat absorbed from the surroundings to maintain the temperature. The formula for the heat transfer (Q) in an isothermal process is given by:

Q = W

Calculating Work Done

The work done (W) by the gas during expansion can be calculated using the formula:

W = nRT ln(Vf / Vi)

• n = number of moles of gas (1 mol in this case)
• R = ideal gas constant (8.314 J/(mol·K))
• T = absolute temperature in Kelvin (0°C = 273.15 K)
• Vi = initial volume (13.0 L)
• Vf = final volume (20.0 L)

Plugging in the Values

Now, let's substitute the values into the work formula:

W = (1 mol) × (8.314 J/(mol·K)) × (273.15 K) × ln(20.0 L / 13.0 L)

First, calculate the natural logarithm:

ln(20.0 / 13.0) ≈ 0.1542

Now, substituting this back into the equation for work:

W = 1 × 8.314 × 273.15 × 0.1542

Calculating this gives:

W ≈ 8.314 × 273.15 × 0.1542 ≈ 3.5 J

Converting to Kilojoules

Since the question asks for the energy transfer in kilojoules, we need to convert joules to kilojoules:

Q = W = 3.5 J = 0.0035 kJ

Final Result

The energy transfer by heat that occurs between the gas and its surroundings during this isothermal expansion is approximately:

0.0035 kJ

This means that as the gas expands from 13.0 L to 20.0 L at a constant temperature of 0°C, it absorbs about 0.0035 kJ of heat from its surroundings to maintain its temperature. This process illustrates the fundamental relationship between work and heat in thermodynamic systems, especially for ideal gases undergoing isothermal changes.