The efficiency of a Carnot engine is determined by the temperature difference between the hot and cold reservoirs. The Carnot cycle is an idealized thermodynamic cycle that consists of four processes: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

Let's analyze the efficiency and work done by the first Carnot engine that operates between 200°C and 0°C.

1. Identifying the temperatures and heat transfer:
- The source temperature (hot reservoir) is 200°C.
- The sink temperature (cold reservoir) is 0°C.
- The working substance absorbs 4 kilocalories (kcal) of heat from the source.

2. Calculating the efficiency of the first Carnot engine:
The efficiency of a Carnot engine is given by the formula:

Efficiency = 1 - (Temperature of the cold reservoir / Temperature of the hot reservoir)

Using the given temperatures:
Efficiency = 1 - (273 + 0) / (273 + 200) = 1 - 273/473 = 1 - 0.577 = 0.423 (or 42.3%)

The efficiency of the first Carnot engine is 42.3%.

3. Determining the useful work done by the first Carnot engine:
The work done by a Carnot engine is given by the formula:

Work = Efficiency * Heat absorbed from the source

Using the given values:
Work = 0.423 * 4 kcal = 1.692 kcal

The first Carnot engine performs 1.692 kilocalories of useful work.

Now, let's analyze the second Carnot engine that operates between 0°C and -200°C.

1. Identifying the temperatures and heat transfer:
- The source temperature (hot reservoir) is 0°C.
- The sink temperature (cold reservoir) is -200°C.
- The working substance absorbs 4 kilocalories (kcal) of heat from the source.

2. Calculating the efficiency of the second Carnot engine:
Efficiency = 1 - (Temperature of the cold reservoir / Temperature of the hot reservoir)

Using the given temperatures:
Efficiency = 1 - (273 - 200) / (273 - 0) = 1 + 73/273 = 1 + 0.267 = 1.267 (or 126.7%)

The efficiency of the second Carnot engine is 126.7%.

3. Determining the useful work done by the second Carnot engine:
Work = Efficiency * Heat absorbed from the source

Using the given values:
Work = 1.267 * 4 kcal = 5.068 kcal

The second Carnot engine performs 5.068 kilocalories of useful work.

In conclusion, the first Carnot engine has an efficiency of 42.3% and performs 1.692 kilocalories of useful work, while the second Carnot engine has an efficiency of 126.7% and performs 5.068 kilocalories of useful work. The efficiency of the second Carnot engine is higher due to the larger temperature difference between the hot and cold reservoirs.

42% N 1.68kcal