An ideal gas expands through an adiabatic process. Which of the following statements is true?

• A. The internal energy of the gas remains constant.
• B. Heat is transferred into the gas from the surroundings.
• C. The temperature of the gas decreases during the expansion.
• D. The pressure of the gas increases during the expansion.

Answer: (C)

Verified step by step guidance

1. Recall that an adiabatic process is one in which no heat is exchanged between the system and its surroundings, so \(Q = 0\).
2. Use the first law of thermodynamics, which states \(\Delta U = Q - W\). Since \(Q = 0\), this simplifies to \(\Delta U = -W\), meaning the change in internal energy equals the negative of the work done by the system.
3. During expansion, the gas does work on the surroundings, so \(W\) is positive, which means \(\Delta U\) is negative; thus, the internal energy decreases.
4. For an ideal gas, internal energy is directly proportional to temperature, so a decrease in internal energy implies a decrease in temperature during expansion.
5. Since the gas expands, its volume increases and pressure typically decreases (assuming no external constraints), so the pressure does not increase during expansion.