Question

An inventor claims to have devised a cyclical engine for use in space vehicles that operates with a nuclear-fuelgenerated energy source whose temperature is 920 R and a sink at 490 R that radiates waste heat to deep space. He also claims that this engine produces 4.5 hp while rejecting heat at a rate of 15,000 Btu/h. Is this claim valid?

Answer 1

Answer:

Valid

Explanation:

to determine if the claim is valid, we compare the efficiency of the device to that of a Carnot engine.

The following data were given

High Temperature = 920R,

Low temperature =490R

work=4.5hp =4.5*2544.5=11450.25Btu/h

low heat Ql heat= 15000Btu/h

High heat Qh=work +Ql=11450.25Btu/h+15000Btu/h=26450.25Btu/h

Next we cal calculate the efficiency of the Carnot engine

$E_Carnot=1-\frac{T_L}{T_H}\\ E_Carnot=1-\frac{490}{920}\\ E_Carnot=0.467$

Hence the maximum efficiency at the given temperature is 47%

Next we calculate the efficiency of the device

$E_device=\frac{work}{Q_H} \\E_device=\frac{11450.25}{26450.25} \\E_device=0.433$

which is 43%

since the maximum efficiency of 47% is not exceeded, we can conclude that the claim is valid