A Carnot engine operates between 170°C and 20°C. How much ice can the engine melt from its exhaust after it has done 6.0 104 J of work?
i need a step by step process. you don't have to give me the answer.
find the efficiency.
Then with efficiency, and work done, find work wasted.
From work wasted, convert to ice melting.
To determine the amount of ice that can be melted from the exhaust of the Carnot engine, we need to follow these steps:
Step 1: Calculate the efficiency of the Carnot engine.
The efficiency (η) of a Carnot engine is given by the formula:
η = 1 - (T_cold / T_hot)
where T_hot is the temperature of the hot reservoir (in Kelvin) and T_cold is the temperature of the cold reservoir (also in Kelvin).
In this case, T_hot = 170°C + 273.15 = 443.15K, and T_cold = 20°C + 273.15 = 293.15K.
Step 2: Calculate the heat entering the system.
The heat entering the system (Q_hot) can be calculated using the equation:
Q_hot = W / η
Given that the work done by the engine is 6.0 × 10^4 J, substitute this value into the equation to find Q_hot.
Step 3: Calculate the heat leaving the system.
The heat leaving the system (Q_cold) is equal to the heat entering the system since no heat is lost or gained in a Carnot engine.
Step 4: Calculate the heat transferred to melt ice.
The amount of heat required to melt ice (Q_melt) can be calculated using the formula:
Q_melt = Q_cold / (heat of fusion of ice)
The heat of fusion of ice is the amount of heat required to convert ice at 0°C to water at 0°C, which is 334,000 J/kg.
Step 5: Calculate the mass of ice melted.
The mass of ice melted (m) can be calculated using the formula:
m = Q_melt / (heat of fusion of ice)
Substitute the values of Q_melt and the heat of fusion of ice into the equation to find the mass of ice melted.
By following these steps, you can calculate the amount of ice that the Carnot engine can melt from its exhaust after doing 6.0 × 10^4 J of work.