In an adiabatic process, which of the following statements is true?

Solution

Physics sir · 4 steps

Adiabatic means no heat at all, so plug Q = 0 into C = Q/(n Δ T) and see what comes out.

1. Meaning of adiabatic. In an adiabatic process no heat enters or leaves the gas, so Q = 0. The temperature can still change, because work is done.

   C = Q/(n Δ T) = 0/(n Δ T) = 0

2. Molar heat capacity. Molar heat capacity is the heat supplied per mole per kelvin of temperature change. Here Δ T ≠ 0 but Q = 0, so C = 0.
3. Check the others. With Q = 0, the first law Q = Δ U + W gives W = -Δ U. So work done by the gas equals the decrease in internal energy, not the increase. For an ideal gas U rises with T, never falls.
4. So. The true statement is (b): the molar heat capacity in an adiabatic process is zero.

The idea to keep. For any process, C = Q/(n Δ T). Adiabatic has Q = 0, so C = 0. Isothermal has Δ T = 0, so C is infinite. Do not mix the two up.

Answer from the NTA final answer key. Solution by PrepWiser.