Solving a 20% Efficient Real Engine Problem

[jaidon]

Homework question:

A 20% efficient real engine is used to speed up a train from rest to 5.00m/s. It is known that an ideal (Carnot) engine having the same cold and hot reservoirs would accelerate the same train from rest to 6.50m/s using the same amount of fuel. Assuming that the engines use air at 27C as a cold reservoir, find the temperature of steam at the hot reservoir.

I think what my real problem is is that I'm not sure what the fact that they use the same amount of fuel is telling me. I know that something will be equal between them besides the cold reservoir, but I'm not sure what. The work can't be the same because the final speeds are different.

Can anyone help me to understand this please? Thanks

 

[Andrew Mason]

Homework question:

A 20% efficient real engine is used to speed up a train from rest to 5.00m/s. It is known that an ideal (Carnot) engine having the same cold and hot reservoirs would accelerate the same train from rest to 6.50m/s using the same amount of fuel. Assuming that the engines use air at 27C as a cold reservoir, find the temperature of steam at the hot reservoir.

I think what my real problem is is that I'm not sure what the fact that they use the same amount of fuel is telling me. I know that something will be equal between them besides the cold reservoir, but I'm not sure what. The work can't be the same because the final speeds are different.

Can anyone help me to understand this please? Thanks

Using the same amount of fuel to accelerate to 6.5 m/s tells you that the ideal Carnot engine would produce 1.69 times more kinetic energy from the same amount of fuel as the real engine does. So it is 1.69 times more efficient.

Since for the Carnot cycle, the efficiency is:
$$\frac{T_H - T_C}{T_H}$$ (temperatures in Kelvins)
and we know that
Efficiency_ideal = 1.69Efficiency_real
you can work out $T_H$.

AM

 

[Clausius2]

Homework question:

A 20% efficient real engine is used to speed up a train from rest to 5.00m/s. It is known that an ideal (Carnot) engine having the same cold and hot reservoirs would accelerate the same train from rest to 6.50m/s using the same amount of fuel. Assuming that the engines use air at 27C as a cold reservoir, find the temperature of steam at the hot reservoir.

I think what my real problem is is that I'm not sure what the fact that they use the same amount of fuel is telling me. I know that something will be equal between them besides the cold reservoir, but I'm not sure what. The work can't be the same because the final speeds are different.

Can anyone help me to understand this please? Thanks

The same problem and the same answer:
https://www.physicsforums.com/showthread.php?t=51671

I think both of you have used the same book.