09. Heat Engine, Carnot’s Cycle and Refrigeration (COP)
Thermodynamics

148553 A Carnot's heat engine works between the temperature $427^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW}$ ?

1 $0.417 \mathrm{kcal} / \mathrm{s}$
2 $4.17 \mathrm{kcal} / \mathrm{s}$
3 $41.7 \mathrm{kcal} / \mathrm{s}$
4 $0.212 \mathrm{kcal} / \mathrm{s}$
Thermodynamics

148554 An ideal engine is working between temperature $400 \mathrm{~K}$ and $300 \mathrm{~K}$. It absorbs 600 cal heat from the source. The work obtained per cycle from the engine is

1 $630 \mathrm{~J}$
2 $630 \mathrm{cal}$
3 $2400 \mathrm{cal}$
4 zero
Thermodynamics

148555 A Carnot engine working between $300 \mathrm{~K}$ and $600 \mathrm{~K}$ has a work output of $800 \mathrm{~J}$ per cycle. What is the amount of heat energy supplied to the engine from source per cycle?

1 $1200 \mathrm{~J} /$ cycle
2 $1600 \mathrm{~J} /$ cycle
3 $1400 \mathrm{~J} /$ cycle
4 None of the above
Thermodynamics

148557 An ideal gas heat engine operates in a Carnot's cycle between $227^{\circ} \mathrm{C}$ and $127^{\circ} \mathrm{C}$. It absorbs $6 \times 10^{4} \mathrm{~J}$ at high temperature. The amount of heat converted into work is

1 $1.6 \times 10^{4} \mathrm{~J}$
2 $1.2 \times 10^{4} \mathrm{~J}$
3 $4.8 \times 10^{4} \mathrm{~J}$
4 $3.5 \times 10^{4} \mathrm{~J}$
Thermodynamics

148558 The efficiency of Carnot engine is $\eta$, when its hot and cold reservoirs are maintained at temperature $T_{1}$ and $T_{2}$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir by keeping the cold one constant at $T_{2}$ is

1 $\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{(\mathrm{~T}-\eta)(1-1.5 \eta)}$
2 $\frac{0.5 \mathrm{~T}_{2} \eta}{(1-1.5 \eta)(1-\eta)}$
3 $\frac{\mathrm{T}_{1}}{(\mathrm{~T}-\eta)}-\frac{\mathrm{T}_{2}}{(1-1.5 \eta)}$
4 $\frac{(1-\eta)(1-1.5 \eta)}{\mathrm{T}_{1} \mathrm{~T}_{2}}$
Thermodynamics

148553 A Carnot's heat engine works between the temperature $427^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW}$ ?

1 $0.417 \mathrm{kcal} / \mathrm{s}$
2 $4.17 \mathrm{kcal} / \mathrm{s}$
3 $41.7 \mathrm{kcal} / \mathrm{s}$
4 $0.212 \mathrm{kcal} / \mathrm{s}$
Thermodynamics

148554 An ideal engine is working between temperature $400 \mathrm{~K}$ and $300 \mathrm{~K}$. It absorbs 600 cal heat from the source. The work obtained per cycle from the engine is

1 $630 \mathrm{~J}$
2 $630 \mathrm{cal}$
3 $2400 \mathrm{cal}$
4 zero
Thermodynamics

148555 A Carnot engine working between $300 \mathrm{~K}$ and $600 \mathrm{~K}$ has a work output of $800 \mathrm{~J}$ per cycle. What is the amount of heat energy supplied to the engine from source per cycle?

1 $1200 \mathrm{~J} /$ cycle
2 $1600 \mathrm{~J} /$ cycle
3 $1400 \mathrm{~J} /$ cycle
4 None of the above
Thermodynamics

148557 An ideal gas heat engine operates in a Carnot's cycle between $227^{\circ} \mathrm{C}$ and $127^{\circ} \mathrm{C}$. It absorbs $6 \times 10^{4} \mathrm{~J}$ at high temperature. The amount of heat converted into work is

1 $1.6 \times 10^{4} \mathrm{~J}$
2 $1.2 \times 10^{4} \mathrm{~J}$
3 $4.8 \times 10^{4} \mathrm{~J}$
4 $3.5 \times 10^{4} \mathrm{~J}$
Thermodynamics

148558 The efficiency of Carnot engine is $\eta$, when its hot and cold reservoirs are maintained at temperature $T_{1}$ and $T_{2}$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir by keeping the cold one constant at $T_{2}$ is

1 $\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{(\mathrm{~T}-\eta)(1-1.5 \eta)}$
2 $\frac{0.5 \mathrm{~T}_{2} \eta}{(1-1.5 \eta)(1-\eta)}$
3 $\frac{\mathrm{T}_{1}}{(\mathrm{~T}-\eta)}-\frac{\mathrm{T}_{2}}{(1-1.5 \eta)}$
4 $\frac{(1-\eta)(1-1.5 \eta)}{\mathrm{T}_{1} \mathrm{~T}_{2}}$
Thermodynamics

148553 A Carnot's heat engine works between the temperature $427^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW}$ ?

1 $0.417 \mathrm{kcal} / \mathrm{s}$
2 $4.17 \mathrm{kcal} / \mathrm{s}$
3 $41.7 \mathrm{kcal} / \mathrm{s}$
4 $0.212 \mathrm{kcal} / \mathrm{s}$
Thermodynamics

148554 An ideal engine is working between temperature $400 \mathrm{~K}$ and $300 \mathrm{~K}$. It absorbs 600 cal heat from the source. The work obtained per cycle from the engine is

1 $630 \mathrm{~J}$
2 $630 \mathrm{cal}$
3 $2400 \mathrm{cal}$
4 zero
Thermodynamics

148555 A Carnot engine working between $300 \mathrm{~K}$ and $600 \mathrm{~K}$ has a work output of $800 \mathrm{~J}$ per cycle. What is the amount of heat energy supplied to the engine from source per cycle?

1 $1200 \mathrm{~J} /$ cycle
2 $1600 \mathrm{~J} /$ cycle
3 $1400 \mathrm{~J} /$ cycle
4 None of the above
Thermodynamics

148557 An ideal gas heat engine operates in a Carnot's cycle between $227^{\circ} \mathrm{C}$ and $127^{\circ} \mathrm{C}$. It absorbs $6 \times 10^{4} \mathrm{~J}$ at high temperature. The amount of heat converted into work is

1 $1.6 \times 10^{4} \mathrm{~J}$
2 $1.2 \times 10^{4} \mathrm{~J}$
3 $4.8 \times 10^{4} \mathrm{~J}$
4 $3.5 \times 10^{4} \mathrm{~J}$
Thermodynamics

148558 The efficiency of Carnot engine is $\eta$, when its hot and cold reservoirs are maintained at temperature $T_{1}$ and $T_{2}$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir by keeping the cold one constant at $T_{2}$ is

1 $\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{(\mathrm{~T}-\eta)(1-1.5 \eta)}$
2 $\frac{0.5 \mathrm{~T}_{2} \eta}{(1-1.5 \eta)(1-\eta)}$
3 $\frac{\mathrm{T}_{1}}{(\mathrm{~T}-\eta)}-\frac{\mathrm{T}_{2}}{(1-1.5 \eta)}$
4 $\frac{(1-\eta)(1-1.5 \eta)}{\mathrm{T}_{1} \mathrm{~T}_{2}}$
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Thermodynamics

148553 A Carnot's heat engine works between the temperature $427^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW}$ ?

1 $0.417 \mathrm{kcal} / \mathrm{s}$
2 $4.17 \mathrm{kcal} / \mathrm{s}$
3 $41.7 \mathrm{kcal} / \mathrm{s}$
4 $0.212 \mathrm{kcal} / \mathrm{s}$
Thermodynamics

148554 An ideal engine is working between temperature $400 \mathrm{~K}$ and $300 \mathrm{~K}$. It absorbs 600 cal heat from the source. The work obtained per cycle from the engine is

1 $630 \mathrm{~J}$
2 $630 \mathrm{cal}$
3 $2400 \mathrm{cal}$
4 zero
Thermodynamics

148555 A Carnot engine working between $300 \mathrm{~K}$ and $600 \mathrm{~K}$ has a work output of $800 \mathrm{~J}$ per cycle. What is the amount of heat energy supplied to the engine from source per cycle?

1 $1200 \mathrm{~J} /$ cycle
2 $1600 \mathrm{~J} /$ cycle
3 $1400 \mathrm{~J} /$ cycle
4 None of the above
Thermodynamics

148557 An ideal gas heat engine operates in a Carnot's cycle between $227^{\circ} \mathrm{C}$ and $127^{\circ} \mathrm{C}$. It absorbs $6 \times 10^{4} \mathrm{~J}$ at high temperature. The amount of heat converted into work is

1 $1.6 \times 10^{4} \mathrm{~J}$
2 $1.2 \times 10^{4} \mathrm{~J}$
3 $4.8 \times 10^{4} \mathrm{~J}$
4 $3.5 \times 10^{4} \mathrm{~J}$
Thermodynamics

148558 The efficiency of Carnot engine is $\eta$, when its hot and cold reservoirs are maintained at temperature $T_{1}$ and $T_{2}$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir by keeping the cold one constant at $T_{2}$ is

1 $\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{(\mathrm{~T}-\eta)(1-1.5 \eta)}$
2 $\frac{0.5 \mathrm{~T}_{2} \eta}{(1-1.5 \eta)(1-\eta)}$
3 $\frac{\mathrm{T}_{1}}{(\mathrm{~T}-\eta)}-\frac{\mathrm{T}_{2}}{(1-1.5 \eta)}$
4 $\frac{(1-\eta)(1-1.5 \eta)}{\mathrm{T}_{1} \mathrm{~T}_{2}}$
Thermodynamics

148553 A Carnot's heat engine works between the temperature $427^{\circ} \mathrm{C}$ and $27^{\circ} \mathrm{C}$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0 \mathrm{~kW}$ ?

1 $0.417 \mathrm{kcal} / \mathrm{s}$
2 $4.17 \mathrm{kcal} / \mathrm{s}$
3 $41.7 \mathrm{kcal} / \mathrm{s}$
4 $0.212 \mathrm{kcal} / \mathrm{s}$
Thermodynamics

148554 An ideal engine is working between temperature $400 \mathrm{~K}$ and $300 \mathrm{~K}$. It absorbs 600 cal heat from the source. The work obtained per cycle from the engine is

1 $630 \mathrm{~J}$
2 $630 \mathrm{cal}$
3 $2400 \mathrm{cal}$
4 zero
Thermodynamics

148555 A Carnot engine working between $300 \mathrm{~K}$ and $600 \mathrm{~K}$ has a work output of $800 \mathrm{~J}$ per cycle. What is the amount of heat energy supplied to the engine from source per cycle?

1 $1200 \mathrm{~J} /$ cycle
2 $1600 \mathrm{~J} /$ cycle
3 $1400 \mathrm{~J} /$ cycle
4 None of the above
Thermodynamics

148557 An ideal gas heat engine operates in a Carnot's cycle between $227^{\circ} \mathrm{C}$ and $127^{\circ} \mathrm{C}$. It absorbs $6 \times 10^{4} \mathrm{~J}$ at high temperature. The amount of heat converted into work is

1 $1.6 \times 10^{4} \mathrm{~J}$
2 $1.2 \times 10^{4} \mathrm{~J}$
3 $4.8 \times 10^{4} \mathrm{~J}$
4 $3.5 \times 10^{4} \mathrm{~J}$
Thermodynamics

148558 The efficiency of Carnot engine is $\eta$, when its hot and cold reservoirs are maintained at temperature $T_{1}$ and $T_{2}$, respectively. To increase the efficiency to $1.5 \eta$, the increase in temperature $(\Delta T)$ of the hot reservoir by keeping the cold one constant at $T_{2}$ is

1 $\frac{\mathrm{T}_{1} \mathrm{~T}_{2}}{(\mathrm{~T}-\eta)(1-1.5 \eta)}$
2 $\frac{0.5 \mathrm{~T}_{2} \eta}{(1-1.5 \eta)(1-\eta)}$
3 $\frac{\mathrm{T}_{1}}{(\mathrm{~T}-\eta)}-\frac{\mathrm{T}_{2}}{(1-1.5 \eta)}$
4 $\frac{(1-\eta)(1-1.5 \eta)}{\mathrm{T}_{1} \mathrm{~T}_{2}}$