G L Mittal and TARUN MITTAL Solutions for Chapter: Carnot's Heat Engine : Second Law of Thermodynamics, Exercise 2: NUMERICALS

A Carnot's engine has the same efficiency $\left(\mathrm{i}\right)$ between $100 \mathrm{K}$ and $500 \mathrm{K}$ and $\left(\mathrm{ii}\right)$ between $T \mathrm{K}$ and $900 \mathrm{K}$ Calculate the temperature $T$ of the sink. $($in kelvin$)$

Calculate the difference in efficiencies of a Carnot's heat engine working between (i) $400 \mathrm{K}$ and $350 \mathrm{K}$ and (ii) $350 \mathrm{K}$ and $300 \mathrm{K}$.

A Carnot's engine works between two temperatures whose difference is $100 \mathrm{K}$. If it absorbs $746 \mathrm{J}$ of heat from the source and gives $546 \mathrm{J}$ to the sink, calculate the temperatures of the source and the sink.

A Carnot's ideal heat engine operates between $227°\mathrm{C}$ and $127°\mathrm{C}$. It absorbs $600$ calories of heat from the source. How much work per cycle is the engine capable of performing? ( $1$ calorie $=4.2$ joule)

A Carnot's reversible engine works with an efficiency of $50\%$. During each cycle, it rejects $150$ calories of heat at $30°\mathrm{C}$. Calculate (i) temperature of the source, (ii) work done by the engine per cycle. $(1 \mathrm{cal}=4.2 \mathrm{J})$.

The temperature of the sink of a Carnot engine is $27°\mathrm{C}$. If the efficiency of the engine is $40\%$, find the temperature of the source.

A reversible engine converts one-sixth of heat absorbed at the source into work. When the temperature of the sink is reduced by $82°\mathrm{C}$, the efficiency of the engine is doubled. Find the temperatures of the source and the sink.

A Carnot engine whose low-temperature reservoir is at $7°\mathrm{C}$ has an efficiency of $50\%$. It is desired to increase the efficiency to $70\%$. By how many degree should the temperature of the high-temperature reservoir be raised?