How Much Ice Melts in a Carnot Engine Cycle?

[jalpabhav]

A Carnot engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. When 6600 J of heat is put into the engine and the engine produces work, how many kilograms of ice in the tub are melted due to the heat delivered to the cold reservoir? (See Table 12.3 for appropriate constants.)

I'm not sure how to being.
I was thinking about using:
Qc/Qh = Tc/Th but I'm not sure :yuck:

 

[OlderDan]

A Carnot engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. When 6600 J of heat is put into the engine and the engine produces work, how many kilograms of ice in the tub are melted due to the heat delivered to the cold reservoir? (See Table 12.3 for appropriate constants.)

I'm not sure how to being.
I was thinking about using:
Qc/Qh = Tc/Th but I'm not sure :yuck:

If you know the reservoir temperatures and the heat input to a Carnot engine, you should be able to calculate the heat output. What equations do you have for the efficiency of a Carnot engine?

 

[m2003]

As a scientist, it is important to approach problems systematically and methodically. Let's first define the variables in this scenario. Qc represents the heat delivered to the cold reservoir, while Qh represents the heat delivered to the hot reservoir. Tc and Th represent the temperatures of the cold and hot reservoirs, respectively.

Using the equation Qc/Qh = Tc/Th, we can rearrange it to solve for the heat delivered to the cold reservoir, Qc. This can be done by multiplying both sides by Qh, giving us Qc = (Tc/Th) * Qh.

Now, we can use the given information to solve for the mass of ice melted. We know that 6600 J of heat is delivered to the engine, which means Qh = 6600 J. We can also look up the values for Th and Tc in Table 12.3. Let's assume that the hot reservoir has a temperature of 100°C (373 K) and the cold reservoir has a temperature of 0°C (273 K).

Plugging these values into our equation, we get Qc = (273/373) * 6600 J = 4800 J. This means that 4800 J of heat is delivered to the cold reservoir.

Now, we can use the heat of fusion of water (333.5 J/g) to calculate the mass of ice melted. We divide the heat delivered to the cold reservoir by the heat of fusion to get the mass of ice melted: 4800 J / 333.5 J/g = 14.4 g.

Therefore, approximately 14.4 grams of ice will melt due to the 6600 J of heat delivered to the engine. It is important to note that this is a simplified calculation and does not take into account any losses or inefficiencies in the engine.