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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# The engine of a large ship does 2.00×108J of work with an efficiency of 5.00% (a) How much heat transfer occurs to the environment (b) How many barrels of fuels are consumed if each barrel produces 6.00×109 J of heat transfer when burned?

Amount of heat transferred to the environment is 3.8×109J and .667 barrels of fuels are consumed.

See the step by step solution

## Step: 1 Introduction-

Heat engine is a device by which a system is made to undergo a cyclic process. It results conversion of heat into work. First and second law helps in the operation of Heat Engine.

## Step: 2 Given Parameters and formula to be used-

Amount of work done by the engine $W=2.00×{10}^{8}\mathrm{J}$

Efficiency $\eta =5.00%$

## Step: 3 Calculations

(a)

Relation to be used

$h=\frac{W}{{Q}_{1}}\phantom{\rule{0ex}{0ex}}W={Q}_{1}-{Q}_{2}$

Here

$h-\mathrm{Efficinency}\mathrm{of}\mathrm{the}\mathrm{heat}\mathrm{Engine}\phantom{\rule{0ex}{0ex}}W-\mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{the}\mathrm{Heat}\mathrm{Engine}\phantom{\rule{0ex}{0ex}}{Q}_{1}-\mathrm{Amount}\mathrm{of}\mathrm{Heat}\mathrm{Extracted}\mathrm{from}\mathrm{Heat}\mathrm{Engine}\phantom{\rule{0ex}{0ex}}{Q}_{2}-\mathrm{Amount}\mathrm{of}\mathrm{Heat}\mathrm{transfered}\mathrm{to}\mathrm{Environment}$

$h=\frac{W}{{Q}_{1}}\phantom{\rule{0ex}{0ex}}{Q}_{1}=\frac{W}{h}\phantom{\rule{0ex}{0ex}}{Q}_{1}=\frac{2.00×{10}^{8}}{.05}\phantom{\rule{0ex}{0ex}}{Q}_{1}=4×{10}^{9}\mathrm{J}$

Further,

$W={Q}_{1}-{Q}_{2}\phantom{\rule{0ex}{0ex}}{Q}_{2}={Q}_{1}-W\phantom{\rule{0ex}{0ex}}{Q}_{2}=4×{10}^{9}J-2.00×{10}^{8}\mathrm{J}\phantom{\rule{0ex}{0ex}}{Q}_{2}=3.8×{10}^{9}\mathrm{J}$

(b) Barrels of fuel consumed -

$n=\frac{4×{10}^{9}\mathrm{J}}{6×{10}^{9}\mathrm{J}}\phantom{\rule{0ex}{0ex}}=0.667$

So, amount of heat transferred to the environment is $3.8×{10}^{9}\mathrm{J}$ and barrels of fuel consumed are $0.667$.