Question

A heat engine operates between 35 C and 330 C. If this engine extracts a total energy of 800 MJ from fuel, then how many MJ of energy could be used as useful mechanical energy? Remember that e = 1 - T(low)/T(high), where T is in Kelvin (= Celsius + 273).

Answer 1

Machine used 392 MJ energy as mechanical energy.

Step-by-step explanation:

Efficiency(e) is defined as the ratio of the work done by the machine to the energy provided to the machine.

`e = (Energy\ Used)/(Energy\ Given)` .....(1)

The efficiency of the machine is also given by the relation :

`e = 1 - (T_(low) )/(T_(high) )` .....(2)

Here T(low) and T(high) denotes the temperature in kelvin.

According to the problem, T(low) = 35⁰ C = 35 + 273 = 308 K

T(high) = 330⁰ C = 330 +273 = 603 K

Substitute the values of T(low) and T(high) in the equation (2).

`e = 1 - (308 )/(603 )`

`e = 1 - 0.51`

e = 0.49

According to the problem, Energy Given = 800 MJ

Substitute the value of efficiency(e) and Energy Given in the equation (1).

`0.49 = (Energy\ Used)/(800 MJ)`

Energy used = 0.49 x 800 MJ = 392 MJ