An ideal gas starts in state A at temperature T. The gas expands to new volume V by an adiabatic process and its final temperature is T′. What is the relationship between T and T′?
A) T < T′
B) T > T′
C) T = T′
D) The answer depends on the heat capacity of the ideal gas.
E) The answer depends on the number of moles of gas and the pressure.
To determine the relationship between T and T′, we need to understand the properties of an adiabatic process. In an adiabatic process, there is no heat exchange between the gas and its surroundings (Q = 0). The relationship between the initial and final temperatures can be determined using the adiabatic equation:
T' = T * (V/V')^(γ-1)
where T is the initial temperature, T' is the final temperature, V is the initial volume, V' is the final volume, and γ is the heat capacity ratio of the gas.
Since the problem doesn't provide information about the specific heat capacity ratio of the gas, we cannot directly calculate the value of T' based on T. Therefore, the answer to the question is option D) The answer depends on the heat capacity of the ideal gas.