A Carnot engine operates between 170°C and 23°C. How much ice can the engine melt from its exhaust after it has done 4.5 104 J of work? _____kg

Use the upper and lower absolute temperatures to compute the Carnot engine efficiency.

Wout/Qin = 1 - (300/443) = 0.3228

Divide 45000 J by the efficiency for the heat energy input, Qin.
Qin = 139400 J

Qout = 139400 - 45000 = 94,400 J

Divide that by the heat of fusion of ice, 334 J/g, for the final answer, in grams. They may want you to convert to kilograms

do i just divide it by a 1000 to convert. Because I am getting the wrong answer

nevermind it is correct. Thank you very much.

To determine the amount of ice that the Carnot engine can melt, we need to calculate the amount of heat absorbed by the engine and compare it to the heat required to melt the ice.

The efficiency (ε) of a Carnot engine is given by the formula:

ε = 1 - (Tc/Th)

where Tc is the temperature of the colder reservoir (in Kelvin) and Th is the temperature of the hotter reservoir (in Kelvin).

To convert the temperatures from Celsius to Kelvin, we add 273 to each temperature:

Tc = 23°C + 273 = 296 K

Th = 170°C + 273 = 443 K

Now we can calculate the efficiency:

ε = 1 - (296 K / 443 K)

Next, we need to find the amount of heat absorbed by the engine. The formula for the heat absorbed (Qh) is:

Qh = W / ε

where W is the work done by the engine.

Qh = (4.5 x 10^4 J) / ε

Now, we need to calculate the heat required to melt the ice. The heat required to melt one kilogram of ice (Qm) is equal to the heat of fusion of ice (Lf):

Qm = Lf

The heat of fusion of ice is approximately 333.55 kJ/kg.

Now we can calculate the amount of ice melted:

Ice_melted = Qh / Qm

Substituting the values we have:

Ice_melted = (4.5 x 10^4 J) / (333.55 kJ/kg)

Remember to convert kilojoules to joules by multiplying by 1000:

Ice_melted = (4.5 x 10^4 J) / (333.55 x 10^3 J/kg)

To simplify the calculation, we can cancel out the factors of 10^4 and 10^3:

Ice_melted = (4.5 / 333.55) kg

Evaluating this expression gives the final result.