A gas is compressed from an initial volume of 5.55 L to a final volume of 1.22 L by an external pressure of 1.00 atm. During the compression the gas releases 124 J of heat. What is the change in internal energy of the gas?

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Identify the initial volume (V_i), final volume (V_f), external pressure (P), and the heat released (q). In this case, V_i = 5.55 L, V_f = 1.22 L, P = 1.00 atm, and q = -124 J (negative because heat is released).

Calculate the work done on the gas using the formula for work done by constant external pressure: W = -P \(\Delta\) V. Here, \(\Delta\) V (change in volume) = V_f - V_i.

Substitute the values into the work formula to find W. Remember to convert the pressure from atm to the appropriate unit if necessary to match the unit of energy in joules.

Use the first law of thermodynamics, which states that the change in internal energy (\(\Delta\) U) of a system is given by \(\Delta\) U = q + W, where q is the heat added to the system and W is the work done on the system.

Substitute the values of q and W into the equation for \(\Delta\) U to find the change in internal energy of the gas.

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주요 개념

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First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed. In the context of a gas, this law can be expressed as 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. This principle is essential for calculating the change in internal energy when heat is exchanged and work is performed.

Work Done on a Gas

Work done on a gas during compression can be calculated using the formula W = PΔV, where P is the external pressure and ΔV is the change in volume. In this case, since the gas is compressed, the work is considered positive from the perspective of the system. Understanding how to calculate work is crucial for determining the overall energy changes in the gas.

Heat Transfer

Heat transfer refers to the energy exchanged between a system and its surroundings due to a temperature difference. In this scenario, the gas releases heat (Q = -124 J), indicating an exothermic process. Recognizing the sign and magnitude of heat transfer is vital for accurately applying the First Law of Thermodynamics to find the change in internal energy.