B M Sharma Solutions for Chapter: Thermodynamics, Exercise 2: CONCEPT APPLICATION EXERCISE

Two Carnot's engines $A$ and $B$ are operated in series. The first one, $A$, receives heat at $800 \mathrm{K}$ and rejects to a reservoir at temperature $T$. The second engine, $B$, receives the heat rejected by the first engine and in turn rejects to a heat reservoir at $300 \mathrm{K}$. Calculate the temperature $T$ for the following situation:

The efficiencies of two engines are equal.

A refrigerator freezes water at $0°\mathrm{C}$ into $10 \mathrm{kg}$ ice at $0°\mathrm{C}$ in a time interval of $30 \min$. Assuming the room temperature to be $20°\mathrm{C}$, calculate the minimum amount of power needed to make $10 \mathrm{kg}$ of ice

A refrigerator whose coefficient of performance is $5$, extracts heat from the cooling compartment at the rate of $250 \mathrm{J}/\mathrm{cycle}$.

(a) How much work per cycle is required to operate the refrigerator?

(b) How much heat is discharged to the room?

A Carnot engine is designed to operate between $480 \mathrm{K}$ and $300 \mathrm{K}$. Assuming that the engine actually produces $1.2 \mathrm{kJ}$ of mechanical energy per kcal of heat absorbed, compare the actual efficiency with the theoretical maximum efficiency.

The efficiency of a Carnot cycle is$\frac{1}{6}$. By lowering the temperature of the sink$65 \mathrm{K}$, it increases too$\frac{1}{3}$. Calculate the initial and final temperatures of the sink.

In which case will the efficiency of a Carnot cycle be higher?

(a) When the temperature of the source is increased by $\mathrm{\Delta }T$.

(b) When the temperature of the sink is lowered by $\mathrm{\Delta }T$?

A Carnot heat engine has an efficiency of $10\%$. If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

In a cold storage, ice melts at the rate of $2 \mathrm{kg} {\mathrm{h}}^{-1}$ when the external temperature is $20°\mathrm{C}$. Find the minimum power output of the motor used to drive the refrigerator which just prevents the ice from melting. Latent heat of fusion of ice $=80 \mathrm{cal} {\mathrm{g}}^{-1}$