Question

A gas is compressed adiabatically, which one of the follwing statement is NOT true.

• A. The change in the internal energy is equal to the work done on the gas
• B. The temperature of the gas increases
• C. There is no heat supplied to the system
• D. There is no change in the internal energy

Answer 1

The Correct Option is D

To understand the correct answer to the question of which statement is NOT true when a gas is compressed adiabatically, let's go through each option systematically.

1. The change in the internal energy is equal to the work done on the gas
   • In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). Based on the first law of thermodynamics: \Delta U = Q + W
   • Since Q = 0, the equation simplifies to: \Delta U = W, meaning the change in internal energy is equal to the work done on the gas.
   • This statement is true.
2. The temperature of the gas increases
   • During adiabatic compression, the work done on the gas results in an increase in internal energy, which is typically observed as an increase in temperature.
   • Therefore, this statement is true.
3. There is no heat supplied to the system
   • The word 'adiabatic' indicates that the process occurs without any heat transfer to or from the system, confirming that Q = 0.
   • This statement is consistent with the definition of an adiabatic process and is true.
4. There is no change in the internal energy
   • As previously explained, in an adiabatic compression, the work done on the gas changes its internal energy.
   • Thus, the internal energy does change, which makes this statement incorrect in the context of adiabatic compression.

Based on the above analysis, the statement that is NOT true for an adiabatic compression is: There is no change in the internal energy.