The second law of thermodynamics states, among other things, that it is impossible for heat to be entirely converted into work in a cyclical process. This means that there will always be some loss of energy in any real, practical system due to inefficiencies such as friction, heat dissipation, etc.
Given the energy added to an engine as heat, [tex]\( Q_{in} = 2.5 \times 10^4 \, J \)[/tex], and the net work done by the engine, [tex]\( W_{net} = 7.0 \, J \)[/tex].
### Calculate the engine’s efficiency:
The efficiency ([tex]\( \eta \)[/tex]) of an engine is given by the ratio of the net work done by the engine to the energy added to the system as heat:
[tex]\[ \eta = \frac{W_{net}}{Q_{in}} \][/tex]
Substituting the given values:
[tex]\[ \eta = \frac{7.0}{2.5 \times 10^4} \][/tex]
Now, let's perform the calculation step-by-step:
1. [tex]\( 2.5 \times 10^4 = 25000 \)[/tex]
2. Divide 7.0 by 25000 to get the efficiency:
[tex]\[ \eta = \frac{7.0}{25000} \][/tex]
[tex]\[ \eta = 0.00028 \][/tex]
Therefore, the engine’s efficiency is 0.00028, which does not match any of the provided choices directly. Hence, this might indicate a misunderstanding or a typo in the problem statement regarding the value of net work done by the engine. It is worth double-checking the given values.
### Determine the correct statement from the second law of thermodynamics:
The second law of thermodynamics implies that energy cannot be entirely converted to work. Therefore, the relevant statement is:
B. Energy added to a system as heat cannot be converted entirely to work.
Given these conclusions:
- The engine’s efficiency based on the provided values is [tex]\( 0.00028 \)[/tex].
- The relevant statement from the second law of thermodynamics is:
B. Energy added to a system as heat cannot be converted entirely to work.
