CALC The temperature of 0.150 mol of an ideal gas is held constant at 77.0°C while its volume is reduced to 25.0% of its initial volume. The initial pressure of the gas is 1.25 atm. (c) Does the gas exchange heat with its surroundings? If so, how much? Does the gas absorb or liberate heat?

Verified step by step guidance

1. Identify the initial conditions and the final conditions of the gas. The initial conditions are: number of moles (n) = 0.150 mol, initial temperature (T) = 77.0°C, which needs to be converted to Kelvin, and initial pressure (P1) = 1.25 atm. The final condition is that the volume is reduced to 25% of its initial volume (V2 = 0.25V1).
2. Convert the initial temperature from Celsius to Kelvin by using the formula T(K) = T(°C) + 273.15. This will give you the temperature in Kelvin, which is necessary for calculations involving the ideal gas law.
3. Apply the ideal gas law in the form P1V1 = P2V2 to find the final pressure of the gas (P2), since the number of moles and the temperature are constant. Rearrange the formula to solve for P2: P2 = P1V1/V2.
4. Analyze the process to determine if there is heat exchange. Since the temperature of the ideal gas remains constant (isothermal process), any work done on or by the gas results in an equal and opposite heat transfer according to the first law of thermodynamics, which states ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.
5. Determine the direction of heat flow. In an isothermal compression (volume decreases), the gas is compressed, so work is done on the gas. According to the first law of thermodynamics, the gas must absorb an amount of heat equal to the work done on it to keep the internal energy constant. Therefore, the gas absorbs heat.

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of an ideal gas through the equation PV = nRT. In this scenario, the gas is held at a constant temperature while its volume changes, which implies that the pressure must also change according to the law. Understanding this relationship is crucial for determining how the gas behaves under the given conditions.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. In the context of the gas, if the volume is reduced while maintaining constant temperature, the gas must do work on the surroundings, which can involve heat exchange. This principle helps in analyzing whether the gas absorbs or releases heat during the process.

Heat Transfer

Heat transfer refers to the movement of thermal energy between systems or surroundings due to a temperature difference. In this case, since the gas is compressed at constant temperature, it may exchange heat with its surroundings to maintain thermal equilibrium. Understanding whether the gas absorbs or liberates heat is essential for answering the question about heat exchange.