Thermodynamics

The efficiency of a Carnot engine is given by the formula: Where: - is the efficiency, - is the temperature of the reservoir (hot body), - is the temperature of the sink (cold body). Now, if the temperature of the reservoir is increased by 50%, the new temperature will be: If the temperature of the sink is decreased by 50%, the new temperature will be: Thus, the new efficiency will be: Simplifying: Since , the original efficiency is . Thus, the new efficiency becomes: Hence, the new efficiency is .

The first law of thermodynamics states: Where:
- is the heat added to the system,
- is the change in internal energy,
- is the work done by the system.
In the process from a to b: So, In the process from b to a, since the work is done on the system: Thus, the change in internal energy from b to a is: The total heat added in the process b to a is: Since the system returns to its original state, this heat is rejected.
Thus, 17.5 kJ of heat is rejected by the system.

The ratio of specific heats is related to the degrees of freedom of the gas molecules by the formula: This relationship arises from the kinetic theory of gases, where the specific heats depend on the number of degrees of freedom. For an ideal gas, this ratio is known to be , where is the number of degrees of freedom. Thus, the correct option is (B).