Question

A steam engine delivers 5.4×108 J of work per minute and services 3.6 × 109 J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?​

Answer 1

Explanation:

Given that,

●Work done by the steam engine, W = 5.4 × $\sf{10^{8} }$J per minute.

●Heat supplied from the boiler, H = 3.6 × $\sf{10^{9}}$J per minute.

Since, Efficiency of the engine:

$\leadsto \sf \frac{Input \: Energy}{Output \: Energy}= \frac{5.4×10 {}^{8} J}{3.6×10 {}^{9} J} \\ \\ \leadsto \sf \: 1.5\: \: \red \bigstar$

Therefore, the percentage efficiency of the engine is 15 %.

Now, the amount of heat wasted ;

$\leadsto\sf(3.6×10^{9} - 5.4× 10^{8}) \\ \\ \leadsto \sf 3.06×10^{9} J. \: \: \green \bigstar$

Therefore the efficiency of the steam engine is 15% and the amount of heat that is wasted per minute is 3.06×$\sf\underline{10^{9 }}$J.

Answer 2

Correct question :

A steam engine delivers 5.4 × 10⁸ J of work per minute and services 3.6 × 10⁹ J of heat per minute from its boiler. What is the efficiency of the engine? How much heat is wasted per minute?​

Solution :

Given that :

• Work done by steam engine = 5.4 × 10⁸ J
• Heat produced = 3.6 × 10⁹ J

To find out :

• Efficiency of engine
• How much heat is wasted per minute

Explanation :

Efficiency of engine is given by,

$: \implies\underline{\boxed{\sf{Efficiency = \bigg(\dfrac{Work \ done}{Energy} \times 100 \bigg) \% }}} \\\\ \\ : \implies\sf Efficiency = \bigg(\dfrac{5.4 \times 10^8}{3.6 \times 10^9} \times 100 \bigg) \% \\\\ \\ : \implies\sf Efficiency = \bigg(\dfrac{5.6}{36} \times 100 \bigg) \% \\\\ \\ : \implies\sf Efficiency = (0.15 \times 100) \% \\\\ \\ : \implies\large\underline{\boxed{\sf{Efficiency = 15 \% }}} \ \bigstar$

$\therefore\underline{\textsf{Efficiency of the engine = {\textbf{15 \% }}}}$

$\rule{280}{1}$

Now heat wasted is given by,

$: \implies\underline{\boxed{\sf{Heat \ wasted = Energy - Work \ done }}} \\\\ \\ : \implies\sf Heat \ wasted = (3.6 \times 10^9) - (5.4 \times 10^8) \\\\ \\ : \implies\sf Heat \ wasted = 3060000000 \ J \\\\ \\ : \implies\large\underline{\boxed{\sf{Heat \ wasted = 3.06 \times 10^9 \ J }}} \ \bigstar$

$\therefore\underline{\textsf{Heat wasted per minute = {\textbf{3.06 \times 10^ ^{\text{9}} J }}}}$