Final answer:
The output at 62% efficiency depends on the total energy input; efficiency is the ratio of work or energy output to energy input. To find the work output, multiply the efficiency by the total energy input. The heat engine's work output and heat transfer to the environment are calculated accordingly based on its efficiency.
Step-by-step explanation:
The output when the efficiency is 62% depends on the amount of heat transfer into the system. Efficiency is defined as the ratio of the work output or energy output to the total energy input. To calculate the actual output, we would need to know the total energy input into the system. For example, if a system has an energy input (Q₁) of 2.50 × 10¹⁴ J and an efficiency of 62%, the work output (W) can be calculated using the formula W = Efficiency × Q₁, which in numbers would be W = 0.62 × 2.50 × 10¹⁴ J.
If we have a heat engine with a specific efficiency, such as 42.0% as in one of the problems, we can determine the ratio of heat transfer to the environment to work output by looking at the remainder of energy that is not converted into work. The work done is directly proportional to the efficiency and the heat input. For example, if a heat engine has an efficiency of 42.0% and the heat transfer into the engine is 6.00x10⁹ J, the work output would be 0.42 × 6.00x10⁹ J.